# David M. Young, Jr.

## Excerpts from Letters for Awarding a Professorship to David M. Young, Jr.

"**Do You Know the 'Great' Professor Young?**"

David R. Kincaid, Computer Sciences Department, The University of Texas at Austin Austin, TX 78712 USA

## Abstract

In support of the nomination of Dr. David M. Young, Jr., to a distinguished professorship, letters were solicited from an impressive group of authorities from around the world. Excerpts from those 1982 letters are presented.

## Introduction

In 1982, Professor David M. Young, Jr., was nominated for the honor of being awarded a distinguished professorship at The University of Texas at Austin; namely, an Ashbel Smith Professor of Mathematics and of Computer Sciences. As part of the process, testimonial letters were solicited by Professor E. Ward Cheney of the Mathematics Department from a large number of top numerical analysts, who were familiar with Young's research, including a dozen or so world famous individuals. (The file containing the letters is in the Archives of American Mathematics at the Center for American History, The University of Texas at Austin. Professor Young passed away on 21 Dec 2008.)

Excerpts from the letters in the file that was compiled at that time give a clear picture of Dr. Young's scientific accomplishments, and the high regard with which he was held in the worldwide scientific computing community.

## Cover Letter

### James W. Daniel

Excerpts from a letter by **James W. Daniel**, who was, at that time, Chair and Professor, Mathematics Department, to Dean Robert Boyer, College of Natural Sciences, The University of Texas at Austin. (21 Dec 1982)

Professor Young's scientific career began in earnest with his Ph.D. dissertation at Harvard in 1950. This dissertation is universally acknowledged to be one of the great milestones in the history of scientific computing. In it, Young introduced an important new class of numerical methods for the solution of partial differential equations and established the efficacy of his methods. The publication of the dissertation in the *Transactions of the American Mathematical Society*, 1954, stimulated an enormous interest in the subject, and the resulting scientific activity continues today undiminished. Methods established by Young are the *work horses* of many computing installations where partial differential equations must be solved routinely; nuclear reactor calculations and oil-field reservoir simulations are two classes of numerical computations where these methods are in constant use.

Young has continued his research with undiminished vigor, even during years when he bore heavy administrative responsibility, such as the years as Head of the Numerical Analysis Group at the Ramo-Wooldridge Corporation and later as Director of the Computation Center here at the University. He has had an uninterrupted flow of research papers and monographs and has supervised the research of numerous Ph.D. candidates. His work is now at the forefront of the interaction between numerical analysis and new computer architectures.

In 1980, at a meeting held at Los Alamos National Laboratory, special note was made of the fact that it was the thirtieth anniversary of Young's important paper, and that current research in numerical methods for partial differential equations is based largely on Young's work, not only in the 1950 paper but also in his later research. Others honor Young: so should we.

Among our present faculty without a named professorship, no one deserves this honor more than David Young. I recommend him strongly.

## U.S.A. Letters

### Randolph E. Bank

Excerpts from a letter by **Randolph E. Bank**, who was, at that time, Associate Professor of Mathematics, University of California, San Diego. (29 Nov 1982)

Dr. Young is one of the most widely known and highly respected numerical analysts in the world. He is the premier expert on the iterative solution of linear systems of equations. His contributions have been extremely valuable, since the solutions of systems of linear equations are the most costly and time consuming components of many important engineering and scientific computations, from the modelling of petroleum reservoirs to the design of integrated circuits.

Dr. Young's professional career began near the dawn of the modern computer era, and thus he was among the first generation of numerical analysts to not only analyze the mathematical properties of numerical methods, but also to consider the algorithmic aspects of their implementations on digital computers. His early work on the successive overrelaxation (SOR) method had a profound influence on the development of iterative methods. SOR and its derivatives and descendants today remain among the most widely used and effective methods for treating many classes of problems.

Dr. Young has a distinguished record of contributions to the development of numerical analysis and the broader areas of computer science and applied mathematics as academic disciplines, highlighted by his role in the formation of the Computer Science Department and the Center for Numerical Analysis at UT.

### Garrett Birkhoff

Excerpts from a letter by **Garrett Birkhoff, **who was, at that time, Professor of Mathematics, Harvard University. Cambridge, Massachusetts. Professor Birkhoff was certainly one of the leading mathematicians of the world. (13 Sept 1982)

It is a pleasure to express my admiration for David Young's distinguished work over the decades. This began with his highly original 1950 Ph.D. Thesis, in which he developed and gave a rigorous theoretical basis for his SOR method (as applied and extended by Varga), which was the most successful method used to design nuclear power reactors in the 1950's.

Since that time, he has continued to design and explore the theoretical properties of iterative methods for solving very large systems of linear equations, especially those arising from elliptic boundary value problems. His 1971 book*Iterative Solutions of Large Linear Systems*, which contains many of his results, is a model of scholarship.

Over the past five years, he has been developing with David Kincaid a systematic collection of subroutines for solving large systems of the kind described above. This collection is called ITPACK; it should prove very helpful as a takeoff point and collection of well-tested building blocks for those designing software for solving elliptic problems, as well as providing carefully analyzed and explained models for students. The new Hageman-Young book *Applied Iterative Methods*, serves as an admirable reference for the underlying theory.

### John R. Cannon

Excerpts from a letter by **John R. Cannon**, who was, at that time, Professor of Mathematics, Washington State University. (3 Nov 1982)

Professor Young is known worldwide for his extensive and lasting contributions to numerical solutions of ordinary and partial differential equations. Some of Professor Young's research has been used by scientists and engineers for over 20 years and I expect this usage to continue throughout the 21st century.

### S. D. Conte

Excerpts from a letter by **S. D. Conte, ** who was, at that time, Distinguished Visiting Professor, Department of the Air Force, Department of Computer Science, USAF Academy. On leave as Professor and Chair, Computer Sciences Department, Purdue University. (23 Jul 1982)

I have know David Young since 1951 when we worked together at the Aberdeen Proving Grounds as newly graduated Applied Mathematicians. Later in 1956 I took a position as a mathematician at Ramo-Wooldridge Corporation in a group headed by Dr. Young. We worked closely on many challenging problems from 1956--1960. I have kept in informal contact with him over the intervening years until the present.

David is undoubtedly best known for his early work on successive overrelaxation and its applications to the solution of large sparse linear systems. He is clearly the nation's leading expert in this important area. His ideas have influenced researchers in the numerical solution of elliptic systems for the past 3 decades. Even more important, his ideas have been incorporated into working programs for solving important problems in such areas as nuclear reaction calculations and diffusion equations. His contributions to both practical and theoretical development of elliptic equation solvers cannot be exaggerated. He is very highly regarded by his peers, and he is in constant demand as a speaker at conferences, universities, and national laboratories.

### John Dennis, Richard Tapia and Mary Wheeler

Excerpts from a letter by **John Dennis, Richard Tapia**, and **Mary Wheeler**, who were, at that time, Professors, Mathematical Sciences Department, Rice University. (8 Dec 1982)

David Young has earned this honor through his research efforts, his teaching and counseling of students, and the visibility he has given the Texas mathematical community. His leadership in the Texas Computation Center and the Center for Numerical Analysis has been outstanding. Not only has be been involved in the development of first rate codes, but in bringing outstanding visitors to the state.

We will not elaborate on each of Young's theoretical papers and textbooks, but wish to point out that his work on SOR procedures for the numerical solution of partial differential equations has not only been mathematically interesting and sound, but has had a profound effect on practical engineering calculations. SOR procedures were used in the numerical simulations for the Alaska pipeline and are used in many reservoir engineering codes. %The importance to the latter area is made apparent by noting the number of papers (Society of Petroleum Engineering (SPE)) interested in vectorization of SOR schemes.

### Richard E. Ewing

Excerpts from a letter by **Richard E. Ewing, **who was, at that time, the J. E. Warren Distinguished Professor of Energy and Environment, Department of Mathematics, University of Wyoming. (9 Nov 1982)

Having held positions in both academy and industry ..., I have had a unique opportunity to see the breadth of impact of Dr. Young's work on the scientific community. He has made significant contributions to many aspects of the numerical solution of partial differential equations. This area of research is central to the process of modeling of a great variety of physical phenomena and to the field of applied mathematics in general.

Dr. Young developed the successive overrelaxation technique for the iterative solution of large systems of linear equations. This method and its variants have formed the standard for industrial use on many problems over a decade. Therefore, Dr. Young is a recognized authority and is highly respected throughout the petroleum industry. ... Another important aspect of the field of numerical solution of partial differential equations is the area of software development. The important advances in solution techniques are made available to the computing community through computer programs. Dr. Young and his colleagues have developed an excellent, widely used, software package ITPACK which %has made an enormous impart on the computing scientific community.

### George J. Fix

Excerpts from a letter by **George J. Fix** , who was, at that time, Professor and Head, Department of Mathematics, Carnegie-Mellon University. Pittsburgh, Pennsylvania. (29 Nov 1982)

David wrote what is universally acknowledged as the best Ph.D. thesis in the entire history of numerical analysis. In this thesis, he developed what is now called S.O.R.

The industrial impact is just as great. There is probably isn't a laboratory or research and development group involved in the numerical solution of partial differential equations that doesn't have some version of S.O.R. in their code library.

Since his thesis, David has played a leadership role in research on the solution of large-scale problems using iterative methods. His book on this subject is a classic.

At this time, there are a number of numerical analysis with Chairs or University Professorships who's impact has been great, but still less than David's. He clearly deserves the position.

### C. W. Gear

Excerpts from a letter by **C. W. Gear** , who was, at that time, Professor of Computer Science and Applied Mathematics, Department of Computer Science, University of Illinois at Urbana-Champaign. (19 Aug 1982)

David has been active for thirty years and has always paid attention to the important practical problems of the times rather than going after the easy abstract results. This started with his involvement in one of the first programmable electronic digital computers built in this country and continues to the present day. in his involvement with ITPACK which is making many of his important theoretical contributions available to the scientific community. His lengthly publication record coupled with four books (two at the research monograph level) also attest to his productivity and his desire to make his work available to the more than an esoteric audience.

### Gene H. Golub

Excerpts from a letter by **Gene H. Golub** , who was, at that time, Professor and Chairman, Department of Computer Science, Stanford University. (2 Aug 1982)

Professor Young's thesis was a landmark in the history of numerical computation. He developed and analyzed a method for solving problems of linear equations arising in the discretization of elliptic partial differential equations. The Successor Overrelaxation Method (S.O.R.) of Young is so widely used that his name and original paper are seldom referenced! It cannot be overstated that the impact of this method on such problems as the design of nuclear reactors has been tremendous.

He has also been involved in the development of other methods for solving linear problems. His books, *Iterative Solutions of Large Linear Systems* and *Applied Iterative Methods* (with L. A. Hageman), are standard references for the scientific community interested in solving structured sparse systems of linear equations.

Excerpts from a letter by **Olin G. Johnson**, who was, at that time, Professor of Computer Science and Director, Research Computation Laboratory, University of Houston. (3 Dec 1982)

David is, indeed, distinguished and highly so. He certainly numbers in the top ten numerical analysts worldwide. Many people, myself, would place him in the top five. In the area of numerical solutions to elliptic partial differential equations, his is number one.

In 1980, at the Elliptic Problem Solvers Conference in Los Alamos, there was a 25th celebration. Twenty-five years of solving such problems on computers. The beginning, 25 years before, was reckoned to be David's Ph.D. dissertation.

### Herb B. Keller

Excerpts from a letter by **Herb B. Keller**, who was, at that time, Professor and Executive Officer for Applied Mathematics, California Institute of Technology. (13 Jul 1982)

Those of us who work in the field of the numerical solution of elliptic differential equations have not the slightest doubt as to the tremendous impact and importance of Young's work in this area. It is truly classic ... Dave has an international reputation ...

He has been one of the early founders of the strong computer science -- numerical analysis combination that has been so successful in the United States.

He has also played an important role as an advisor to government laboratories and as an educator in founding the strong numerical analysis group at your university.

### Peter D. Lax

Excerpts from a letter by **Peter D. Lax**, who was, at that time, Professor, Courant Institute of Mathematical Sciences, New York University. (10 Aug 1982)

Young is certainly regarded by the Numerical Analysis community in America as one of its founding fathers. He has made basic contributions to the numerical solutions of partial differential equations, introducing new ideas over a period of 25 years. The problem he chose turned out to be extremely important and the method of solution he has invented and refined has been astonishingly useful in other contexts as well.

### Olvi L. Mangasarian

Excerpts from a letter by **Olvi L. Mangasarian**, who was, at that time, John von Neumann Professor of Mathematical and Computer Sciences, Computer Science Department, University of Wisconsin--Madison. (2 Nov 1982)

Even though my area, Mathematical Programming, is different from David's area, Numerical Analysis, my research has benefited in a direct way from David's elegant and masterful work on iterative methods. In fact successive overrelaxation methods are just beginning to be applied seriously to mathematical problems. For large problems they may present the only method of solution and hence constitute a very significant advance. In my opinion David Young deserves a great deal of credit for putting these methods on a sound mathematical footing and making them available to people in related fields.

### Seymour V. Parter

Excerpts from a letter from **Seymour V. Parter**, who was, at that time, President, SIAM Society for Industrial and Applied Mathematics and Professor, Department of Mathematics, University of California Berkeley. (17 Sep 1982)

When one begins to think about David Young and his impact on present day numerical analysis one is somewhat taken aback. All of us who work or have worked on iterative methods for elliptic difference equations know of the fundamental and far reaching contributions contained in his paper

While a lot of people have done a lot of very good work on this topic in the almost 30 years since that paper appeared, it is still required reading for anyone wishing to become involved in this subject. As I get older and more aware of how people evolve, mature and develop more sophisticated views of their subject I am more and more impressed that David did that work so early in his career.

But, while that paper may be the paper which first comes to mind, it is by no means the end of the story. No, it is only the opening paragraph. ...A quick glance over this publication list brings out three important facets of David Young's working career.

1) He has continued a deep and penetrating interest in this fundamental area of the solution of the %algebraic problems arising from elliptic partial differential equations.

2) There are many important papers which made truly significant contributions to this area ...

3) His interest in not limited to the *purely theoretical*. David clearly understands the significance of applied problems and the importance of the development of appropriate software. The work on SPADE and ITPACK are strong evidence of his early and continuing good judgement and pioneering efforts in this directions.

### Henry H. Rachford, Jr.

Excerpts from a letter by **Henry H. Rachford, Jr.**, who was, at that time, Professor Emeritus, Department of Mathematical Sciences, Rice University. (28 Oct 1982)

I have known David and his work since first becoming interested in related areas in the mid 1950's. His studies of and development in the use of Successive Overrelaxation (SOR) methods for elliptic difference equations have had a profound influence from the outset. The physical problem areas generating such equations are pervasive in science and engineering, and the SOR methods developed and analyzed by David are almost always considered as one of the reliable methods of solution.

Since David's original work on SOR a large number of competing methods for solving this difficult computational problem have been posed, some of them by him. Almost invariably in any discussion of a competing method a comparison of the computational work estimates as the problem size increases will be made with SOR. This of course means that the original SOR method remains a standard by which more recent developments are measured.

As so frequently happens with a really significant development in science, the original method has many derivatives. One of the more important of these is a symmetric version of SOR called SSOR. This warrant is not only a successful procedure for elliptic equations in it sown right, but in recent years has been used as an effective preconditioned for conjugate gradient methods. Other variants of the SOR approach which are still in great favor for computation are the block SOR and block SSOR methods. These are popular most especially for problems involving quite large numbers of unknowns.

Not only did David do the original work in SOR, for which he is perhaps best know, he has been active for 30 years in related fields. He is a recognized authority on iterative methods, having coauthored two books on this subject.

David Young's impact on the computability of solutions to engineering problems has been quite large in fields known well to me. These include problems in petroleum reservoir engineering. ... Because such problems play a vital role in the conservation, recovery and development of vital national resources, the contributions of David's work to contemporary computation continues to be significant.

### Werner C. Rheinholdt

Excerpts from a letter by **Werner C. Rheinholdt**, who was, at that time, Andrew W. Mellon Professor of Mathematics, University of Pittsburgh. (29 Nov 1982)

David is an internationally respected senior numerical analyst whose work on iterative methods for the numerical solution of partial differential equations has had and continues to have a profound impact on the field. This began already with his paper ... in 1954 which stimulated an entirely new approach toward the study of these methods and belongs among the most seminal and widely quoted papers in numerical analysis. Since then he has contributed numerous deep results to the area. It would be impossible here to go into any details of his numerous publications. His book on iterative solution of large linear systems has become a standard and his more recent work on convergence acceleration and adaptive iterative methods culminated in another book on applied iterative methods which is receiving wide attention.

David was also very influential in the development of educational programs in the computer area. For example, he was a member of the by now famous committee which prepared the very influential recommendations for undergraduate programs in computer science. He also wrote together with R. Gregory, a two volume text on numerical analysis which corresponds to some of the committee recommendations.

### John R. Rice

Excerpts from a letter by **John R. Rice**, who was, at that time, Professor of Mathematics and Computer Sciences, Purdue University. (24 Aug 1982)

His work on iterative methods has had an impact on my work since the 1950's, when I became involved in numerical computation. I regard him as the world's leading authority in this area, a view that I believe is widely shared. ... Furthermore, the ITPACK project (with David Kincaid) is another step in bringing the power of his methods into widespread use. This software package is superior; it will have perhaps as much impact as any single piece of work that David has done. In summary, David's career began with a ``bang*and he is still* producing results which have great impact and importance. He is probably the best known active numerical analyst in the world; he certainly is in the top three or four in terms of overall accomplishments and influence on his work.

### Martin H. Schultz

Excerpts from a letter by **Martin H. Schultz**, who was, at that time, Professor of Computer Science, Yale University. (8 Oct 1982)

David is one of the premier numerical analysts in the world today. Most of his research has been on the solution of large sparse linear systems of equations by iterative methods such as the SOR or conjugate gradient methods. As you know, almost all large-scale scientific computing problems have within them a compute intensive kernel consisting of the numerical solution of such systems. This is particularly true of the numerical solution of partial differential equations, the application which has benefited most directly from David's research.

David is possibly the world's foremost expert on the design, analysis, and practical aspects of iterative methods for solving sparse linear systems. ... His dissertation at Harvard in 1950 established SOR as an iterative method which could be easily implemented on a computer and mathematically analyzed. In particular, he showed how to choose the iteration parameter to optimize the rate of convergence of the method. This dissertation is probably the single most important piece of work in the field of iterative methods for linear systems. Its impact would be very difficult to overestimate. Since 1950 there have been hundreds, perhaps even thousands, of papers which use and build on David's results. Perhaps, even more important, in practical computations SOR is still the dominant method. David has continued his productive research since 1950 and is highly visible in the numerical analysis, mathematical sciences, and scientific computing communities.

I have heard David lecture many times. His style is excellent and he always has a lot to say. My high regard for him is best illustrated by the fact that he has a standing invitation to visit Yale and give a seminar anytime he is in the northeast. I think he has been here virtually every year since our department was formed in 1970.

### G. W. Stewart

Excerpts from a letter by **G. W. Stewart, ** who was, at that time, Professor of Computer Science, University of Maryland. (21 Jul 1982)

David supported me very generously when I began my career as an assistant professor at the University of Texas, and this has left me with very warm feelings toward him as a person. Fortunately, David's record speaks for itself, and all I have to do is to summarize his work.

One of David's most important contributions has been his steadfast advocacy of iterative methods during the seventies, when they are in eclipse. Although the direct methods developed during that decade have proven to be a valuable tool, their importance has been exaggerated, and there is now a tendency to use them in conjunction with iterative methods. David with his recent work on ITPACK and the the method of conjugate gradients has helped foster this marriage.

### Gilbert Strang

Excerpts from a letter by **Gilbert Strang** who was, at that time, Professor, Mathematics Department, Massachusetts Institute of Technology. (1 Dec 1982)

There is a special respect for him, which comes partly form the great contributions he has made. His theory of successive overrelaxation is in first place; it was one of the big steps in the history of numerical analysis. It does not often happen that a single paper gives so beautiful a solution to a question about numerical algorithms. That happens elsewhere in mathematics, but David's work brought it about here, and a hundred researchers have developed and applied his ideas. I would also like to single out his books, among his recent work, as remarkable. It is no small task to do the writing he has done, and his four books are absolutely full of detailed analysis and elegant mathematics.

### Richard S. Varga

Excerpts from a letter from **Richard S. Varga** , who was, at that time, University Professor and Director of the Institute for Computational Mathematics, Kent State University, Kent, Ohio. (14 Jul 1982)

I have known David for exactly thirty-two years, and he has always been a giant in the field of iterative solutions of large sparse linear equations. His thesis (from Harvard University in 1950) developed an extremely deep relationship between the eigenvalues of the successive overrelaxation iterative matrix and the eigenvalues of the associated Jacobi iteration matrix. This relationship (i.e., $(\lambda + \omega - 1 )^2 = \lambda \omega^2 \mu^2$) is now known throughout the world as *Young's equation* and appears in every book on numerical analysis.

Since his first great success (mentioned above), he has continued as a steady producer of first-rate contributions in this field, as can be amply seen from his list of publications. Now, every professional meeting, however remotely associated with numerical analysis, seeks his presences to ensure *success*.*I*n addition, his papers and lectures are always very carefully prepared; he is a professional in every sense of the word, and is universally recognized for his research work. If one person, because of his knowledge and contributions, were to be given the title of *Mr. Iterative Methods*,the overwhelming choice for this title would be David Young. This world-wide recognition of his research has obviously brought credit to the University of Texas at Austin.

### Olof Widlund

Excerpts from a letter by **Olof Widlund**, who was, at that time, Professor of Computer Science, Courant Institute of Mathematical Sciences, New York University. (15 Sep 1982)

David M. Young Jr.'s first contributions to numerical analysis date back to the now classical period around 1950. Among these the work on conformal mapping and the SOR method are still very much worth returning to. His classical result on successive over-relaxation method is for very good reasons the best known result in the now large literature on iterative solutions of linear systems of algebraic equations. His contributions to the latter field span his entire scientific career and include two excellent monographs.

Of his many accomplishments his papers on the symmetric successive over-relaxation method deserve special attention. This work was central in turning this method into a practical tool of numerical computation. He has been very active in the last decade and contributed very significantly to the development of generalized conjugate methods and numerical software.

All his work meet the highest standard of scholarship and his writing is a model of clarity.

## Foreign letters

### Leslie Fox

Excerpts from a letter from **Leslie Fox**, who was, at that time, Professor and Director, Oxford University Computing Laboratory, England. (27 Jul 1982)

I believe that I first met David in 1950 on my first visit to the United States. For over 30 years, I have seen him at regular intervals and have followed (with interest and enjoyment and with great respect) the series of technical papers and books which he has produced in what could only be called a *steady stream* since about that date.

He is without doubt one of the world's leading numerical analysts. He has given research lectures by invitation virtually everywhere of any importance, and he has served with distinction on important international committees. Among these I would mention particularly the committee for the Gatlinburg conferences (probably the most important of these) which have taken place roughly every three years since about 1956. The early ones were in America, but a recent one was in Munich and the 1981 meeting was in Oxford. David has helped the organization of many of these meetings and he is one of the few who has been invited to give a contributory talk to every one of them (except possibly the first which I did not attend!), and invitations to the Gatlinburg meeting are highly prized.

Of his 70 or so papers and 4 books the great majority, at least on the research side, have concerned the numerical solution of structured sets of algebraic linear equations. The particular structures have largely derived from the finite-difference or finite element discretization of elliptic or parabolic partial differential equations. David's crucial contribution in this field was in the invention of the iterative method which assumed the title S.O.R. (successive over-relaxation) and of the properties of some structured matrices, for example the famous*Property A*, *w*hich made possible a rigorous theory on the convergence of this method and the determination of the associated over-relaxation parameter*.*

I believe that this work was the subject of his Ph.D. thesis, and since then he has contributed paper after paper on extensions and generalizations of this basic technique, not only in the rich theoretical area but also in the production of good computer software for the treatment of sparse linear systems which is one of the major problems of the last twenty years. His major achievements in this field are summarized in two books, and two other books on a Survey of Numerical Analysis reveal his comprehensive knowledge of most of this subject. In this subject, moreover, he gives masterly lectures at both teaching and research level, and it is always a pleasure to listen to him.

There is really nothing I need add which would improve the case for this award. David has without doubt made very significant contributions in one main area of numerical analysis, he is in the top few of the world's experts in this area, and his name is well known to all, in all parts of the world, who have done any sort of computation.

### Peter K, Henrici

Excerpts from a letter by **Peter K, Henrici**, who was, at that time, Professor of Mathematics, Eidgenoessische Technische Hochschule, Zurich, Switzerland. (16 Jul 1982)

I am delighted to provide testimony on the profound influence which David's work has had on modern numerical partial differential equations. David's contributions in this area are numerous and profound. However, I wish to single out for special comment his paper, *Iterative methods for solving partial differential equations of elliptic type, *which appeared in 1954 in the*Transactions of the American Mathematical Society*. To the best of my knowledge, this was the first paper concerned with questions of numerical computation that ever appeared in these *Transactions*. It was considered a landmark then, and it still must be so considered today.

By the standards of what was known at that time, this paper signified a quantum leap of progress in the efficiency of constructively solving partial differential equations. This fact was, first of all, of fundamental practical importance. Countless large-scale numerical computations, in reactor theory and in other fields, must have profited from Dave's work, and computing time worth countless thousands of dollars must have been saved. There must be references to Dave's theory of successive over-relaxation all over the scientific literature.

But Dave's theory not only turned out to be singularly useful. In addition, it is a gem of pure mathematics. Whenever I teach numerical solution of partial differential equations, I never fail to present a thorough discussion of Dave's SOR theory, and I as well as my students always are delighted by the sheer elegance and beauty of this particular piece of mathematical research. Although concrete, the theory is by no means trivial, as is know to anyone who has tried to improvise lectures on the subject.

David's fundamental paper has given rise to a large number of attempts to improve on his results and, in particular, to widen the scope of its applicability, which originally was restricted to matrices with that famous *Property A.*While there have been a number of interesting results, including some by Dave himself, nobody has really succeeded in improving the basic results of the 1954 paper which today must be regarded as *classical*.

It sometimes has seemed to me that Dave Young did not quite get the share of international recognition that is due to him on the basis of his contributions to numerical mathematics and, indeed, to science.

### John R. Whiteman

Excerpts from a letter by **John R. Whiteman**, who was, at that time, Professor and Chairman of the Department of Mathematics, and Director of the Institute of Computational Mathematics, Brunel University, England. (6 Dec 1982)

In research in any academic field there are from time to time contributions which stand out as milestones and which change significantly the course of subsequent research activity in the particular field. One such discovery in the field of the numerical solution of elliptic partial differential equations is the fundamental paper by David Young on Successive Over-Relaxation methods for solving the systems of linear equations arising from the finite difference discretization of Laplace problems. This work which was produced in the early 1950's, completely dominated the field of iterative methods for elliptic partial differential equations for the next 20 years. Many variants of the SOR technique have since been produced and all of these build on David Young's fundamental work.

## Industrial Letters

### Louis W. Ehrlich

Excerpts from a letter by **Louis W. Ehrlich**, who was, at that time, Research Mathematician, Milton S. Eisenhower Research Center, The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland. (14 Jul 1982)

David's contributions started with his dissertation and has continued smoothly ever since, as indicated by his many publications. He discovered the Successive Overrelaxation (SOR) Method for the solution of those linear systems of equations which are usually derivable from elliptic partial differential equations. That method is, today, probably the most popular technique for solving such linear systems. Indeed, all other iterative iterative methods are compared to it.

He is considered a leading expert in differential equations. This is evident from the fact that he has been repeatedly invited to contribute chapters on the numerical solutions of elliptic and parabolic partial differential equations to several texts. This eventually led to his first published book.

It should be also pointed out that he is a dedicated and conscientious educator. His second and third books were widely used numerical analysis texts.

David's stature in the Numerical Analysis community can probably be illustrated with the following story. Professor George Forsythe was to give a talk at the June 1972 SIAM Meeting in Philadelphia entitled *A Survey of Modern Numerical Analysis*. As the time approached, Professor Forsythe realized that he would be physically unable to present the talk (he died in April) and suggested a few alternates, foremost among them David Young. The fact that the committee chose him so promptly is indicative of the esteem in which colleagues hold him. David's development in numerical analysis paralleled the development of the field itself.

### Louis A. Hageman

Excerpt from a letter by **Louis A. Hageman**, who was, at that time, Advisory Mathematician, Westinghouse Electric Corporation, Bettis Atomic Power Laboratory, West Mifflin, Pennsylvania. (14 Jul 1982)

Professor Young's contributions to the development and understanding of iterative procedures is internationally recognized by both the industrial and academic communities. His now famous thesis, written in the early 1950's, introduced mathematicians to the beautiful body of theory surrounding iterative procedures. Since that time, he has continued to make important contributions to various branches of mathematics, especially in the area of numerical procedures for the solution of partial differential equations. The underlying computational and theoretical principles of iterative methods developed by Professor Young has been extremely useful to me as an industrial mathematician and as a *user* of iterative procedures in scientific computations.

### Donald W. Peaceman

Excerpt from a letter by **Donald W. Peaceman, **who was, at that time, Senior Research Advisor and mathematician, Exxon Production Research Company, Houston, Texas. (29 Oct 1982)

I am very happy to be able to testify to the value of David Young's work in the area of iterative numerical analysis. My first recollection of him is his landmark work in 1954 on the analysis of SOR (successive overrelaxation) for the solution of elliptic partial differential equations. This work provided the basis for analysis and use of the more powerful LSOR (line SOR) which is now widely used by the oil industry for solving the simultaneous equations that arise in reservoir simulation. I have found his survey papers written in the early 1960's, as well as his books on iterative methods, to be excellent references, and feel that they have had a profound influence on the field of numerical analysis.

Finally, I number among my personal acquaintances several of his students. Their excellent training in numerical analysis, and the contributions they continue to make, is testimony to David's teaching ability.

### Donald J. Rose

Excerpts from a letter by **Donald J. Rose**, who was, at that time, mathematician, Bell Laboratories, Murray Hill, New Jersey. Formerly, Rose was a Professor of Mathematics at Harvard University. (8 Sep 1982)

I have known David since my graduate schools days at Harvard and have many occasions to interact with him. His work on iterative methods has motivated myself and generations of numerical analyst. As you know David is the world's leading expert on successive overrelaxation methods. These methods are powerful. I have applied such methodology in a non-linear iteration to solve major problems in semiconductor simulations.

David continues to be both a productive researcher and a leader in numerical analysis. His work on ITPACK is important; his recent book with Lou Hageman is a rare gem.

### Eugene L. Wachspress

Excerpts from a letter by **Eugene L. Wachspress**, who was, at that time, research scientist, Knolls Atomic Power Laboratory, General Electric Company, Schenectady, New York. (2 Aug 1982)

During the past thirty years my own researches have been related to Dave's and we have maintained a continual exchange of ideas. Dave' thesis was a cornerstone for analysis of iterative solutions of elliptic systems and his subsequent researches have guided our eternal search for greater efficiency.

I first met Dave at Dahlgren, Va., at which time he consulted on use of block overrelaxation for solution of our multigroup diffusion equations. Since that time we have applied Dave's analysis on several generations of scientific computers. The successive overrelaxation method which he has championed over the years is the workhorse for our reactor physics computations.

I have often sought Dave's guidance and was in fact reviewing application of one of his suggestions to work I am now doing on foundations for numerical solutions of the Naiver-Stokes equations when I received your letter.

## University of Texas at Austin Letters

### Graham F. Carey

Excerpts from a letter by **Graham F. Carey**, who was, at that time, Professor, Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin (5 Nov 1982)

I have know David personally these past several years at the University of Texas but knew of his work in iterative methods some years prior to joining the faculty here. His work on ordering and *Property A*, as he termed it, is fundamental to the analysis of iterative methods for elliptic problems. His books on iterative methods consolidate his research and that of others in this important area of numerical analysis. Dr. Young has also been the guiding force in development of the ITPACK library of iterative schemes.

### W. W. Bledsoe

Excerpts from a letter by **W. W. Bledsoe**, who was, at that time, Ashbel Smith Professor of Mathematics and Computer Science, The University of Texas at Austin. (11 Nov 1982)

I have known David for about 20 years and have a high regard for him and his work. He has been a highly respected colleague in both Mathematics and Computer Science, since I joined the University some sixteen years ago. He was the person most responsible for setting up the University Computation Center and in establishing the Computer Sciences Department.

I am not conversant with the research in his area, numerical analysis, but I am aware of his international reputation. Over the years, I have watched a steady stream of eminent scientists come through here to visit him and his group. He seems to be most highly regarded for his pioneering work on iterative solutions of partial differential equations, and for his four books and some 70 papers.

### Robert Todd Gregory

Excerpts from a letter by **Robert Todd Gregory**, who was, at that time, Professor of Mathematics, Professor and former Chair, Computer Science, University of Tennessee, Knoxville. (27 Jul 1982)

[Drs. Gregory and Young worked together for many years at The University of Texas at Austin.]

I joined David at UT six months after he arrived there in Fall 1958. At that time the Computation Center was almost non-existent. They had acquired an IBM 650 and David, I, and a secretary shared a single office next to the computer room.

Within 18 months David, on the basis of his reputation alone, got the first $400,000 grant from NSF towards the purchase of a CDC 1604, the first transistorized computer. (It beat the IBM 7090 into production by one month.) Thus, UT went from nothing to a first class Computation Center in one big jump. Then in 1966, after acquiring a building to house the CDC 1604, and after it became saturated with users, David (again on his reputation alone) got the first $1,000,000 grant from NSF towards the purchase of a CDC 6600. This, again, put UT at the front of the line as far as University Computing Centers go. UT was the first university to have a 6600 and this put them ahead of Berkeley, Stanford, MIT, Harvard and all the rest.

I could not have done this; you could not have done this; but David Young did it.

### Robert Todd Gregory

Excepts from an additional letter submitted by **Robert Todd Gregory** about his work with Dr. Young in the Compuation Center at The University of Texas at Austin. (24 Aug 1982)

During the sixteen years we spent together in Austin, I came to know David very well. I have always respected him as a person and as a professional colleague, and I have never ceased to be amazed at the impact he has made on the world of numerical mathematics.

Many important results in mathematics bear the name of their discovers. However, when David Young discovered the *Successive Overrelaxation Method, *he modestly gave it the abbreviated name *SOR Method*, and it is a pity that his abbreviated name is used exclusively, and we never see it referred to as*Young's SOR Method.*

David's reputation as a scholar is well known to numerical mathematicians around the world and his reputation contributes a great deal to UT Austin. No matter where I go in Europe, the people I meet associate me with David Young because of the two-volume book we wrote together. They invariably assume that I am still at Texas because they know that David Young is there.

David's publication record speaks for itself. Despite his years as an administrator, he has maintained a steady flow of research papers, all of high quality. His *Iterative Solutions of Large Linear Systems* became a classic within a very short time following its publication.

Finally, I must mention David's reputation as a teacher-scholar. He has always had the respect of his students, and those who have been lucky enough to have had him direct their theses and dissertations have an outstanding loyalty to him both as friend and mentor.

### Linda J. Hayes

Excerpts from a letter by **Linda J. Hayes**, who was, at that time, Assistant Professor, Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin. (12 Oct 1982)

I must address David Young as a person. Not only is he intelligent and well respected professionally, but he is above all a gentleman and a man of honor. Many times I have heard colleagues at other campuses comment about how pleasing it is to work with David Young. He is at all times pleasant and dependable, and his work is always top quality.

I had worked for David Young for some years. I can testify to his high and uncompromising standards in research and publications. He motivates those around him to strive for excellence. Dr. Young has served on numerous committees and advisory groups, and his ideas and opinions are well received and respected by his peers.

### David R. Kincaid

Excerpts from a letter by **David R. Kincaid**, who was, at that time, Associate Director, Center for Numerical Analysis, University of Texas at Austin. (11 Oct 1982)

I believe that Dr. Young deserves much of the credit for the outstanding computing facilities at The University of Texas at Austin. As Director of the Computation Center from its beginning in the late 1950s until the early 1970s, he did the basic work that established the Center and set the direction for future developments.

### Winfred P. Lehman

Excerpts from a letter by **Winfred P. Lehman**, who was, at that time, Ashbel Smith Professor, Department of Linguistics, The University of Texas at Austin. (17 Nov 1982)

Dave has contributed greatly to the University by his work as director of the Computation Center in its early days. I was a member of the Faculty Computer Committee during his tenure, and observed at first hand his dedication in bringing about a fine center in computation here at the University. That dedication and the success of the Center are ample grounds for the appointment. In addition, as you pointed out, he has a excellent publication record. Since his field is totally different from mine, I can only comment on the length

I might add an anecdote. When I was president of the Association for Computational Linguistics there was a joint meeting of the AFIPS presidents, at that time of the New York World Fair. For that meeting eminent scholars in computation were brought in from all countries. I still remember a conversation with a Japanese scholar. In the course of it, he learned that I was from the University of Texas, and then he asked me whether I know the great Professor Young. I assured him that I did indeed. I don't remember the Japanese scholar's name, but I'm sure he would join me in seconding your recommendation.

### J. Tinsley Oden

Excerpts from a letter by **J. Tinsley Oden, **who was, at that time, Carol and Henry Groppe Professor of Engineering, Department of Aerospace Engineering and Engineering Mechanics, Texas Institute for Computation Mechanics, The University of Texas at Austin. (20 Jul 1982)

As is well known in the mathematical world, David's unusual competence as a mathematician became first known when he published his outstanding dissertation on iterative methods. He has since established an international reputation as a leader in iterative methods for the solution of linear systems of equations, and his books and papers have had a significant impart on the subject in the intervening years. He is, of course, the founder and director of the Center for Numerical Analysis and an important figure to the numerical analysis community. He has been especially supportive of applications involving computational work, and is a frequent participant in related seminars and colloquia in the Engineering School, which are devoted to computational methods. Moreover, he has been kind enough to participate with me and other colleagues on research proposals that have been instrumental in supporting our graduate program and in building up the level of graduate study in this general area at the university.

David is highly respected by all who know him. He is a gentle person, with an excellent personality, and very easy to get along with. However, he has the strength and conviction to provide important leadership in all phases of academic life.

### Byron D. Tapley

Excerpts from a letter by **Byron D. Tapley**, who was, at that time, W. R. Woolrich Professor, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin. (2 Dec 1982)

As an engineer who is faced with the use of mathematics to solve problems in the ever more difficult aerospace environment, I am particularly appreciative of David's contributions to the area of computational mathematics. Although my impression from discussion with mathematicians external to the University is that David is best know for his work in numerical methods for solving partial differential equations, I personally have considerable appreciation for his contributions to the area of the solution to large linear systems characterized by sparse coupling matrices. While David's contributions to the research literature have been extremely important, he has made a comparable contribution through his several books. In particular, *A Survey of Numerical Mathematics*, which he co-authored with Robert Gregory, are especially important contributions to the literature.

Beyond David's technical contributions, he has been a hard working and influential member of the University of Texas academic community. His former administrative work in helping establish the outstanding Computation Center (which currently exists at the University of Texas) was an important contribution to the research community of the University at large. He has also played a highly visible role in furthering the excellence of the applied mathematics effort at the University.

### Charles H. Warlick

Excerpts from a letter by **Charles H. Warlick**, who was, at that time, Director, Computation Center, and Senior Lecturer, Department of Computer Sciences, The University of Texas at Austin. (17 Dec 1982)

I have worked with Professor Young for 30 years (!) and have had the highest respect for him---both personally and professionally---throughout the years. In fact, we worked together at Aberdeen Proving Ground in 1952 on some of this country's earliest computers, solving elliptic partial difference equations using iterative techniques. We wrote a paper together on the use of Richardson's method which was published by the Ballistics Research Laboratories in 1953.

Our relationship continued when Dr. Young served as my (master's) thesis advisor in 1955 at the University of Maryland. Our paths separated for 10 years as I went into industry where I continued to work in the field of iterative solutions of large linear systems deriving from subsonic air flow around jet engines. I maintained contact with Dr. Young through those years and received much useful advice from him about my work. Dr. Young founded the Computation Center here at UT Austin in 1958, and the Center has had an excellent reputation in the academic computing community from its beginning. I joined the Center as associated director to Dr. Young in 1965 and worked as his principal assistant until 1970. At that time the Center for Numerical Analysis was formed with Dr. Young as director, and I succeeded him as director of the Computation Center. In the intervening years, we have continued to be in frequent contact.

David Young is well known throughout the mathematical world for his pioneering work in successive overrelaxation techniques in the solution of large linear systems and for his continued research and publications in iterative techniques. As a worker in his research field, I have come to know many of Dr. Young's professional colleagues throughout this country and in Europe, and I can state that he is highly respected.

## David M. Young, Jr., Instructorship

To honor his memory, The University of Texas at Austin has established the *David M. Young, Jr., Instructorship in Computational and Applied Mathematics* to support young postdoctoral researchers. Those wishing to contribute to this endowment may send donations to

University of Texas at Austin, College of Natural Sciences - Office of Dean Development Office: DMY Instructorship in Math 1 University Station G2500 Austin, TX, 78712-0548 USA

Please note that many employers match charitable contributions by employees.

For questions, contract the College of National Sciences Development Office by email giving@cns.utexas.edu or by telephone 001 (512) 471-3299.

## Bibliography

D.M. Young, *Iterative Methods for Solving Partial Difference Equations of Elliptic Type*. Ph.D. thesis, Harvard University, Mathematics Department, Cambridge, MA, USA, May 1950.

D.M. Young, *Iterative methods for solving partial difference equations of elliptic type*. Transactions American Mathematical Society, 76: 92--111, 1954.

D.M. Young,*Iterative Solutions of Large Sparse Solutions*. Computer Science and Applied Mathematics series. Academic Press, New York, NY, USA, 1970. 570pp. (Republished by Dover, Mineola, NY, USA, 2003.)

D.M. Young's Web page: http://www.ma.utexas.edu/CNA/DMY/

D.M. Young and R.T. Gregory, *A Survey of Numerical Mathematics*, Volume I. Addison-Wesley Publishing Co., Reading, MA, USA, 1972. 543pp. (Republished by Dover, Mineola, NY, USA, 2003.)

D.M. Young and R.T. Gregory, *A Survey of Numerical Mathematics*, Volume II. Addison-Wesley Publishing Co., Reading, MA, USA, 1973. 659pp. (Republished by Dover, Mineola, NY, USA, 2003.)

L.A. Hageman and D.M. Young, *Applied Iterative Methods*. Computer Science and Applied Mathematics series. Academic Press, New York, NY, USA, 1981. 386pp. (Republished by Dover, Mineola, NY, USA, 2003.)