**Richard Varga**'s parents were both Hungarians who had emigrated to the United States and settled in Cleveland. This city was a good choice since at this time Cleveland had a large number of Hungarian immigrants.

*Encyclopaedia Britannica*records:-

Varga writes [8]:-By1920large numbers of Italians, Poles, Hungarians, Russians, and other groups had come to Cleveland ...[which]became Ohio's most ethnically diverse city. ... The city's culture eventually was enriched by some50groups with different languages and backgrounds. Many new Roman Catholic and Eastern Orthodox churches, as well as synagogues, were built.

Let us note thatMy father was an expert tool and die maker, having learned his trade in Hungary, and my mother was an expert in passementerie[fancy edging or trimming on clothing or upholstery]sewing, and she also worked as a secretary at a local Hungarian newspaper(Szabadság).

*Szabadság = Liberty*was "An American newspaper in the Hungarian language." It was published in Cleveland, Ohio by E T Kohányi from 1910 onwards.

Now Varga's father knew from experience that working with tools was a dirty job and he wanted his son to have a better and cleaner life. He felt that a draftsman would be an ideal trade and Richard was educated with this profession in mind. However, his mother also hoped that one day her son might attend college, so this route was also kept open to him in his schooling in Cleveland. He attended West Technical High School in Cleveland where, to satisfy both parent's hopes and desires, he majored in drafting but also took courses to prepare him for admission to a college. Continuing to follow the same path, he entered Case Institute of Technology in Cleveland with the intention of majoring in mechanical engineering. The Case School of Applied Science, founded in 1880, was renamed the Case Institute of Technology in 1947, about the time Varga entered it, and became part of Case Western Reserve University in 1967. In his second year the Case Institute of Technology introduced a mathematics degree and, having already realised that this was his favourite subject, Varga changed to major in mathematics. He found time for sport as well as studying and was a member of the college wrestling team. He obtained his B.S. in mathematics in June 1950 and then received some excellent advice [8]:-

Varga explains in [8] that his father was not at all happy to lend him money to continue with his education since he had already spent sixteen years at his studies. However, he had his mother to support him and she persuaded his father to lend him $1,500 to fund his first year of graduate studies. He completed his Master's Degree in this first year and was awarded an A.M. in June 1951. Also in 1951 he married Esther Marie Pfister; they had one daughter. He continued to undertake research at Harvard with Joseph Leonard Walsh as his thesis advisor. He was also influenced by Garrett Birkhoff and, after Varga completed his doctorate, they collaborated on a number of research projects which led to a number of joint publications. For his doctoral studies, Varga studied approximation theory for complex analytic functions being awarded a Ph.D. in June 1954 for his thesis... an older professor at Case, Professor Max Morris, asked me what I planned to do. I said that I was to take a job in Cedar Rapids, Iowa, as an actuary.(I had taken courses in statistics and probability.)He said to me, "I have had you as a student in several classes, and I think you should apply to Harvard University for graduate work in mathematics. It's too late now to get any financial assistance from Harvard, but if you can borrow money from your father for the first year of graduate work at Harvard, I am quite sure that you will receive scholarships and financial support for the remaining years of your studies." Then, he looked at me, smiling, and said, "Bet on yourself!" Following his advice, I applied in late July,1950, and was accepted for graduate work in September in mathematics at Harvard University

*Properties of a Special Set of Entire Functions and Their Respective Partial Sums*. Varga explained in [8] how he came to spend six years for working at the Bettis Atomic Power Laboratory in Pittsburgh:-

We mentioned above Varga's joint work with Garrett Birkhoff who he first got to know at Harvard. In fact Birkhoff worked as a consultant for Bettis so this provided the opportunity for their collaboration. Their joint papers include:On finishing at Harvard, I received teaching offers from several colleges in the Cleveland area, but the Korean war was on, and, being1A in the draft, I fully expected to be drafted into the Army after taking such a teaching position. But, by chance, a mathematician, Henry L Garabedian(who had been a professor of mathematics at Northwestern), had taken a job with the Bettis Atomic Power Laboratory in Pittsburgh, and he came to Harvard to recruit people to Bettis, to work on problems related to nuclear reactors; the government deemed such work as "essential". He was absolutely convincing on how exciting it was, working hand-in-hand with engineers, physicists, and the newly emerging "computers". I took the chance and joined the staff at Bettis in June,1954, immediately after getting my Ph.D., and it was a truly exciting experience for me! The problems to be solved on the computers were two- and three-dimensional multigroup diffusion equations, used to design nuclear reactors for submarines, and aircraft carriers, for example, as well as large land-based electric power generators.

*Reactor criticality and non-negative matrices*(1958),

*Implicit alternating direction methods*(1959), and

*Discretization errors for well-set Cauchy problems*(1965). We note that, of course, Varga was undertaking research relevant to nuclear reactors, but we also note that he had changed from being an analyst interested in complex variable to a numerical analyst handling applied mathematical problems. By the time the third of the above mentioned joint papers was written, Varga was no longer working for Bettis for, in 1960, he accepted the position of Professor of Mathematics at Case Institute of Technology. In 1969 he moved to Kent, Ohio, when he was appointed at Kent State as Professor of Mathematics. The year after he arrived was a difficult one at Kent State University for in May 1970 four students who were protesting against the Vietnam War on the University campus were shot dead by the Ohio National Guard. At Kent State, Varga was Director of the Institute for Numerical Mathematics from 1980 to 1988, and from 1988 to 2006 he was Research Director. In 2006 he retired from teaching and was named Professor Emeritus.

Let us look at some of the books that Varga has published. They are *Matrix iterative analysis* (1962), *Functional analysis and approximation theory in numerical analysis* (1971), *Topics in polynomial and rational interpolation and approximation* (1982), (with Albert Edrei and Edward B Saff) *Zeros of sections of power series* (1983), *Scientific computation on mathematical problems and conjectures* (1990), and *Gerschgorin and his circles* (2004). We give some extracts from reviews of these works, beginning with *Matrix iterative analysis* quoting from J H Bramble [3]:-

A O Garder writes:-Professor Varga's book is very clearly written and contains a large amount of quite recent material. ... 'Matrix Iterative Analysis' belongs in the personal library of every numerical analyst interested in either the practical or theoretical aspects of the numerical solution of partial differential equations.

Gene Golub, reviewing the second edition, explains that the 1962 edition [7]:-The iterative procedures for solving finite-difference approximations to second-order partial differential equations of elliptic and parabolic types have been described in many places. This book is the first comprehensive treatment of these procedures which is mathematically rigorous. ... The book is well and clearly written, has an extensive bibliography, and is supplied with numerous problems. It should become a standard text in advanced numerical analysis courses.

Reviewing... became an instantaneous "classic." It was important because it brought together relevant elements of matrix theory and numerical analysis. The book also developed results that were not easy to find in other sources.

*Functional analysis and approximation theory in numerical analysis*, J Burlak writes:-

Charles K Chui writes in a review ofThis book is based on lectures given at Boston University in July1970and is dedicated to the sixtieth birthday of Garrett Birkhoff. Its centre of gravity coincides with that of the title: this is a book on approximation theory. However, the title should prepare the reader for a modern treatment(thoroughly imbedded in functional analysis), for the subject not to be regarded merely as an end in itself(the numerical solution of elliptic and parabolic boundary value problems is the author's eventual target)and for theoretical depth(there are no details of explicit numerical procedures).

*Topics in polynomial and rational interpolation and approximation*:-

Several interesting topics on approximation and interpolation by polynomials and rational functions that fall in the area of complex analysis are presented in these beautifully written lecture notes. In many cases numerical results and graphs are included to illustrate certain results and conjectures. It is interesting to see how numerical computation can help in sharpening ideas and stimulating research in working with problems of various topics in approximation theory.

*Zeros of sections of power series*is described by Walter Hengartner as a 'remarkable monograph' but perhaps the greatest praise is heaped on

*Scientific computation on mathematical problems and conjectures*. George Fix writes [5]:-

Herman te Riele writes:-Let me state at the outset that this monograph is a gem. It contains six completely independent chapters devoted to six different areas. The unifying theme is that all of the problems are drawn from classical analysis with a strong tilt toward approximation theory. The unique part of the monograph is how high-precision numerical calculations can play a creative role in this area. In fact, it is possibly fair to say that the monograph is a sequence of challenging and interesting problems, where both hard analysis and sophisticated computing techniques are brought to bear to develop rigorous proof of interesting conjectures, or in some cases, used to establish counterexamples.

Varga's most recent book,This book contains fascinating accounts of how some long-standing mathematical problems could be solved after an accumulation of efforts by many mathematicians and the use of highly accurate floating-point computations. At the same time it shows that there are still a lot of unsolved mathematical problems, the solution of which may require deep mathematics, but probably also fast computers and highly-accurate numerical software.

*Gerschgorin and his circles*, was reviewed by L Elsner who writes [4]:-

Varga has received many honours including the Hans Schneider Prize from the International Linear Algebra Society:-The new book of Varga contains, along with several new results, nearly all that has been discovered about eigenvalue inclusions since1931. These results are perhaps not at the center of attention of mathematicians nowadays, but the book is interesting enough to merit thorough review and the recommendation to read and use it.

The Prize was awarded in 2005. He has also received the President's Medal from Kent State University in 1981, and the von Humboldt Prize in 1982. The University of Karlsruhe awarded him an honorary degree in 1991, and he received a similar honour from the University of Lille two years later.... for research, contributions, and achievements at the highest level of Linear Algebra.

As to Varga's interests outside mathematics we quote from [2]:-

Richard Varga, however, is not only a great scientist but also a wonderful human being. He is even known to be a serious table tennis player, he is a former wrestler, he likes to repair his car by himself, and anybody who has heard him sing can tell you about his beautiful and powerful voice. His knowledge of languages and flair for telling jokes and anecdotes all contribute to make Richard Varga a very charming man, and he is always "the life and soul of the party."

**Article by:** *J J O'Connor* and *E F Robertson*

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