# Gene Howard Golub

### Quick Info

Chicago, USA

Stanford, USA

**Gene Golub**was an Amercian mathematician who worked in numerical linear algebra.

### Biography

**Gene Golub**'s mother was Bernice Gelman and his father was Nathan Golub. Bernice was from Latvia and emigrated to the United States in 1923, going to Chicago where her sister lived. Nathan was from Zhitomir in the Ukraine and he also emigrated to the United States in 1923, also going to Chicago where he had a brother. Both Nathan and Bernice were Jewish. They were not well educated, coming from relatively poor families. They met for the first time in Chicago and later married, having two sons with Alvin the older and Gene the younger. The language spoken in their home was Yiddish but, after he began his schooling, his parents tried to speak English on occasions. Golub spoke of his upbringing [3]:-

My father, through the years that I can remember, sold bread. ... He would get up early in the morning and collect lots of bread from the bakery and then distribute it either to homes or to mom-and-pop shops. His day was somewhat different - he didn't work on Saturday, this was a Jewish bakery. My mother went to work when I was about five years old and going to kindergarten. In fact, I went to kindergarten just a half-year earlier than necessary because my mother wanted to go to work. She worked in making boys' caps. That was a big industry in Chicago then. ... She spent a good part of her life sewing the interiors of baseball caps.Golub's home was not in the Jewish area of Chicago, but he attended Haugan Elementary School which was in the Jewish area. Especially after World War II began, he suffered anti-Semitism and had a stressful journey to school every day. From the age of twelve he attended Roosevelt Junior High School which involved a longer journey each day. He spoke of the school [3]:-

There were some good teachers and a lot of poor teachers, too. Maybe they faced discipline problems, but I don't think we were especially difficult kids. It was a nice school. It was boys and girls all together; it was coed. I had friends, but almost nobody was interested in science.He proved to be a reasonably good pupil but in no way stood out although mathematics was his best subject. One reason for not shining at school may have been that he had to work to make money which he did selling shoes and working in a pharmacy. The family were too poor to let him buy tickets to attend concerts and the theatre so he worked as an usher to see performances a few times a year. After four years at Roosevelt Junior High School he decided that he would like to be a teacher. The family could not afford to provide funds for him to live away from home so his options were limited. He entered Wright Junior College, spending two years there. He then matriculated at the University of Chicago, still living at home. This gave him two problems. First he had a journey of about and hour and a half to reach the university so this gave him three hours travelling time each day. Second his education up to that point had not prepared him well for a university course. There were other problems too; he had no room of his own at home so studying was difficult. He decided to leave home and complete his university studies at the University of Illinois where one of his friends had gone. He graduated with a B.S. in the spring of 1953.

In his final semester Golub had taken the Digital Computer Programming course and he was offered a position as an assistant in the computing laboratory. In addition to this half-time position he took courses for his Master's Degree. He was awarded his M.A. in mathematical statistics in 1954. A report written on his achievements as a part-time research assistant for the first six months of 1954 reads:-

Mr Golub has been studying the problems associated with factor analysis and is also working on other problems associated particularly with matrix operations. He has programmed Rao's Maximum Likelihood Factor Analysis Method, and has obtained new results, which he will publish. This summer, he presented a paper on tests of significance in factor analysis at the International Psychological Congress in Montreal, and in September will present another at the meeting of the American Psychological Association in New York.Had it not been for the Korean War, Golub may have ended his education at this point but remaining at the University of Illinois to study for a doctorate allowed him to get a draft deferment. He then undertook research for a doctorate with Abraham Taub as his thesis advisor. He was awarded a Ph.D. in 1959 for his thesis

*The Use of Chebyshev Matrix Polynomials in the Iterative Solution of Linear Equations Compared to the Method of Successive Overrelaxation*which developed ideas in a paper by von Neumann. Golub criticised his thesis supervisor [3]:-

Taub didn't know that field so well himself. He just put me into it. So I was no longer doing statistics, although I was getting my degree in statistics, I was doing numerical analysis. ... I was subject to a lot of abuse by Taub. He would just yell and scream at me. ... I think the weaker you are as a person, the more he hammered at you. He was really a nasty piece. At any rate, I finished the thesis.Following the award of his doctorate, Golub had a number of short-term posts. During 1959-60 he was an NSF Fellow at the Mathematical Laboratory at the University of Cambridge in England. There he worked with Maurice Wilkes' EDSAC II group, sharing an office with William Kahan. During that year he collaborated by mail with R S Varga on his first major paper

*Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods*which they published in two parts in 1961. Returning to the United States he was employed at University of California, Lawrence Radiation Laboratory during 1960-61, then spent 1961-62 as a member of the technical staff of the Space Technology Laboratories, Inc. The next two years, 1962-64, he spent as Visiting Assistant Professor in the Computer Science Division at Stanford University. He was invited by Eugene Isaacson to spend the year 1965-66 at the Courant Institute of Mathematical Sciences, New York University where he was an Adjunct Assistant Professor. After this year he returned to Stanford University as an Associate Professor. He spent the rest of his career at Stanford, being promoted to full professor in 1970. He was Chairman of the Stanford University Computer Science Department during 1981-84.

After publishing a few papers such as

*Bounds for eigenvalues of tridiagonal symmetric matrices computed by the LR method*(1962),

*Bounds for the round-off errors in the Richardson second order method*(1962),

*On a lower bound for the rank of a partitioned square matrix*(1963), and

*Comparison of the variance of minimum variance and weighted least squares regression coefficients*(1963), his next highly significant work was

*Numerical methods for solving linear least squares problems*(1965). He said [3]:-

That paper had a great influence on a lot of people, even though it in some sense was well-known before. For instance, Lawson and Hanson referred to that very often.It is impossible in an article such as this to give a full description of his work for he was extremely prolific publishing over 250 books and papers. We simply look briefly at some of his books. In 1983 he published

*Matrix computations*written jointly with Charles F Van Loan:-

Numerical linear algebra is a large and expanding subject which has a growing impact in mathematics and computer science. As the authors declare in the preface, they have written the present book in order to impart a sense of unity to this exciting field.In 1980 Golub lectured on the numerical solution of large linear systems at a summer school in France. The lectures formed the basis of the book

*Résolution numérique des grands systèmes linéaires*published in 1983 as a joint work with Gérard A Meurant who filled in many details and proofs. The main topics covered are the method of least squares, fast Poisson solvers, and iterative methods.

In 1992 Golub, jointly with James M Ortega, published

*Scientific computing and differential equations*. The authors write in the Preface:-

A large part of scientific computing is concerned with the solution of differential equations, and thus differential equations are an appropriate focus for an introduction to scientific computing. The need to solve differential equations was one of the original and primary motivations for the development of both analog and digital computers, and the numerical solution of such problems still requires a substantial fraction of all available computing time. It is our goal in this book to introduce numerical methods for both ordinary and partial differential equations with concentration on ordinary differential equations, especially boundary value problems. Although there are many existing packages for such problems, or at least for the main subproblems such as the solution of linear systems of equations, we believe that it is important for users of such packages to understand the underlying principles of the numerical methods. Moreover, it is even more important to understand the limitation of numerical methods: 'black boxes' cannot solve all problems. Indeed, it may be that one has several excellent black boxes for solving classes of problems, but the combination of such boxes may yield less than optimal results.The same two authors published

*Scientific computing: An introduction with parallel computing*in the following year. Translations of these two books into German appeared in 1995 and 1996. Then in 2005, jointly with Moody T Chu, Golub published

*Inverse eigenvalue problems: theory, algorithms, and applications*.

The list of honours Golub received for his outstanding contributions is too long to list here. Let us simply list those universities that awarded him an honorary degree: Linköping University (1984), University of Grenoble (1986), University of Waterloo (1987), The University of Dundee (1987), University of Illinois (1991), Universitat Louvain (1992), University of Umea, Sweden (1995), Australian National University (1996), Rostov State University, Rostov, Russia (2002), Hong Kong Baptist University (2002).

He had accepted an honorary degree from Eidgenössische Technische Hochschule Zürich (ETH) which he was due to receive on 17 November 2007, the day after he died. The events surrounding his death are described by Philipp Birken:-

On his trip to China two weeks ago, Gene had apparently got flu, which was readily fixed by a doctor with antibiotics. However, his condition got worse nevertheless, he was feeling generally unwell and in particular his legs hurt very much. On Sunday, I drove him to the hospital, where they thought that he had a thrombosis from the long distance flight and kept him there for further tests. Still, he was hoping he could fly to Zürich on Wednesday, as he was very excited about the honorary degree the ETH was going to award him. On Tuesday, they diagnosed Leukemia. They gave him a life expectancy of half a year if he chose a light treatment or much longer if he opted for a four weeks chemotherapy. His situation worsened unexpected and dramatically during the night from Thursday to Friday and he passed away in the morning in the presence of some of his best friends.As to Golub's personality, Trefethen writes in [5]:-

Golub was a bachelor for most of his life, and his colleagues were his family. No family ever had a more loving, attentive or exasperating father. As he liked to say, "Every numerical analyst has a second home at Stanford". Countless colleagues enjoyed a glass of wine at his home there, and hundreds of them stayed over for a night or even a month at his invitation. How did he remember all our birthdays and reading tastes and children's names? Golub could not spend a day without other people. He would eat dinner with them, talk matrices with them, organize conferences with them, write papers and books with them, argue academic politics with them - an endless dance of interactions, plans and projects. Anywhere in the world, a numerical analyst knows who is meant by 'Gene'. About 250 of them were his co-authors. They knew that it would fall to them to do most of the writing; but Golub saw the connections, knew the literature, and made the paper happen. ... Gene Golub was restless and never entirely happy. He was a demanding friend; behind his back, we all had Gene stories to tell. It was a huge back: Gene was big, dominating any room he was in, and grew more impressive and imposing with the years. Graduate students around the world admired and loved him, and he bought them all dinner when he got the chance.

### References (show)

- R H Chan, C Greif and D P O'Leary (eds.),
*Milestones in matrix computation: selected works of Gene H Golub, with commentaries*(Oxford University Press, Oxford, 2007). - Gene Howard Golub in memoriam,
*BIT***48**(1) (2008), 1-2. - T Haigh, An interview with Gene Golub on 22 and 23 October 2005 at Stanford, California,
*Society for Industrial and Applied Mathematics*(2005). - J Markoff, Gene H Golub, an Innovator in Early Computing, Dies at 75,
*New York Times*(10 December 2007). - L N Trefethen, Obituary: Gene H Golub (1932-2007) : Mathematician and godfather of numerical analysis,
*Nature***450**(962) (13 December 2007).

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update December 2008

Last Update December 2008