Gene Golub Remembered

January 6, 2008

Gene Golub, 1932–2007

Michael Heath

The SIAM community lost one of its leading lights when Gene Golub passed away on November 16, 2007. He had been diagnosed with acute myeloid leukemia only a few days earlier. Gene's principal scientific legacy is his technical and personal leadership in establishing the central position of matrix computations in modern scientific computing. His overall legacy is far broader, however, because of his unique role in unifying and establishing a spirit of openness, collegiality, and collaboration in the scientific computing research community worldwide. Gene was also a major player in the evolution of SIAM, having founded two SIAM journals (SISC and SIMAX), served on both the SIAM Council and the SIAM Board of Trustees, and served a term as SIAM president.

Gene will be especially missed as the unofficial but universally recognized "social chairman" for the entire field of numerical analysis. In performing this function, Gene maintained an international travel schedule that was almost legendary---typically, he was home for only a brief stop between trips to Hong Kong and Zurich at the time of his death. Gene was especially known for his encouragement and mentoring of young researchers just becoming established in the field. The combination of Gene's intellectual leadership and his uniquely socializing personality made him a father figure---or perhaps a favorite uncle---to many in scientific computing, and they in turn formed an enormous surrogate family for him, which of course made them related to each other as well. As a consequence, the news of Gene's sudden illness and unexpected death sent a shock wave through the scientific computing community worldwide, and life without his inspiring leadership, generosity, and warmly encouraging presence seemed incomprehensible to many.

Gene's scientific productivity was staggering and his impact profound. He published more than 170 journal articles with an immense number of co-authors, countless conference papers and technical reports, and several books, including the monumental treatise Matrix Computations, written with Charles Van Loan, which has remained the definitive reference on this topic through multiple editions since its original publication in 1983. Another remarkable aspect of Gene's productivity is its uniformity throughout his long and illustrious career. For example, the graduation dates of his thirty PhD students, many of whom went on to highly successful and influential careers of their own, span the years from 1966 to 2007. The only significant gap in this otherwise unbroken string coincided with Gene's terms as chair of Stanford's Computer Science Department (1981–1984) and president of SIAM (1985–1987). Indeed, including his service as director of Stanford's Scientific Computing and Computational Mathematics?(SCCM) program (1988–1998), Gene held major administrative roles for eighteen consecutive years, not to mention his extensive activities as an editor of journals and books and organizer of conferences, making his copious research output all the more amazing.

With their phenomenal range, Gene's research contributions touched almost every corner of numerical linear algebra and its applications. An enumeration of some of them would have to begin with the singular value decomposition, which is arguably the most powerful tool, both theoretically and computationally, in numerical linear algebra. Gene not only provided the first viable, robust algorithm for computing the SVD (in collaboration first with Velvel Kahan and then with Christian Reinsch), but he also pioneered many of the most fundamental applications of the SVD to a host of problems in linear algebra, statistics, and other fields. Gene also established QR factorization as the algorithm of choice for linear least squares and related problems in computational statistics. His work with Paul Concus, Dianne O'Leary, and others established the preconditioned conjugate gradient algorithm and the closely related Lanczos algorithm as the prototypes and cornerstones of modern Krylov subspace methods for linear systems and eigenvalues. Gene's other pioneering contributions, too numerous to describe in detail here, include algorithms for total least squares, numerical techniques for generalized cross-validation, fast Poisson solvers, methods for updating matrix factorizations, Gaussian quadrature rules, methods for inverse eigenvalue problems, and, most recently, acceleration of the page rank algorithm for searching the Web and applications of linear algebra to machine learning.

Naturally, a career of this magnitude produced many well-deserved honors for Gene, including membership in the U.S. National Academy of Sciences, and National Academy of Engineering, and the American Academy of Arts and Sciences, as well as honorary degrees and awards from a host of other scholarly institutions worldwide. Special conferences were held in honor of his 60th (Minneapolis, 1992), 70th (Zurich, 2002), and 75th (Stanford, 2007) birthdays. The latter conference also honored the 50th anniversary of the founding of Stanford's Computer Science Department, in which Gene played an important role. The conference at Stanford was an especially sweet and nostalgic experience for Gene, as hundreds of his friends, family, and other colleagues from around the world converged on Stanford to honor him, exchange warm reminiscences about him, and coincidentally deliver a series of outstanding technical talks that lived up to the high standards that Gene set for our field. We didn't know it at the time, of course, but the conference also turned out to be a valedictory, coming only a few months before Gene's death.

Most of the foregoing recapitulation of the major milestones in Gene's career could be gleaned from his CV and as such does not capture what it was really like to work with Gene or be a member of his inordinately large circle of friends and professional colleagues, so I would like to digress now into a more personal reminiscence on some of my own experiences with Gene, which I suspect are fairly representative of his personal touch with many others.

I first met Gene in the summer of 1973 at my first-ever SIAM meeting (naturally), held in Hampton, Virginia. Gene was a plenary speaker, and due to a failure of the air-conditioning system at the conference hotel, the first talk I ever heard him give was in a nearby movie theater (at least there was a screen handy for the overhead projector). With a bachelor's degree in mathematics, I was working at the time as a scientific applications programmer at Oak Ridge National Laboratory, where, under the influence of Alston Householder and other colleagues, I had gained a keen interest in numerical linear algebra. Upon hearing that I planned to enter graduate school the following year, Gene encouraged me to apply to Stanford. His enthusiasm helped me overcome my doubts about the seemingly daunting odds, and I was indeed admitted to Stanford's PhD program in computer science for the fall of 1974.

I first visited Stanford in the summer of 1974 to arrange housing for the fall. Though I was a mere grad student (really not even that yet), Gene invited me to stay in his home during my visit, and he also invited me to give the NA Seminar (about which more later) that week. In other words, I was treated just as royally as his many distinguished visitors and guests before I had even begun my student career! This seemed very strange and wonderful to me, but it was typical of Gene: Everyone seemed to be equal in his eyes, and all were treated with equal respect.

I returned in the fall to join the NA group, at the time located in a small but comfortable building called Serra House, which had been the Stanford president's home seventy years earlier. Faculty and students were quartered closely together, with everyone on a first-name basis. George Forsythe had passed away a couple of years earlier, but Joe Oliger had just joined the faculty, with a specialization in numerical PDEs that complemented Gene's interest in numerical linear algebra. The steady stream of visiting faculty included such distinguished figures as Jim Wilkinson, Germund Dahlquist, John Dennis, Dick Tapia, Richard Brent, and many others, plus a host of shorter-term visitors from every corner of the globe. Most of the dozen or so graduate students would also go on to become well known, but of course we didn't know that at the time. Such an intellectual hothouse in academia would normally come with a substantial quota of clashing egos, but the atmosphere in Serra House was uniformly collegial and mutually supportive, thanks largely to the tone set by Gene.

The weekly NA Seminar in Serra House was a remarkable institution in itself. Thanks to the stimulating and attractive atmosphere that Gene had fostered, virtually everyone who was anyone in numerical analysis would visit Stanford and speak in this venue at some point during a typical student's graduate career. In attendance were not only faculty and students, but also numerous regulars from local industry. Gene was famous for introducing the audience to the speaker, calling each audience member by name from memory, even the rare attenders whom no one else knew. I recall the students being impressed that Gene could sometimes sit seemingly sleepily through a particularly arcane presentation and still somehow cut right to the heart of the matter with a cogent question at the end. Following the seminar, most of the audience would join Gene and the speaker for a festive dinner at one of the many local Chinese restaurants, whose managers all seemed to be personal friends of Gene's.

After I completed my course work and necessary exams, working with Gene as my PhD thesis adviser was a stimulating and rewarding experience. His role as mentor was finely balanced---very supportive but not dominating. He adapted to each student individually, and was happy to suggest a thesis topic or to allow the student to find his or her own way. I chose a topic in nonlinear optimization that was not particularly close to Gene's direct research interests; nevertheless, at our weekly meetings he listened perceptively to my progress reports and invariably offered helpful advice, direction, and pointers to relevant research literature. After completing my PhD and returning to Oak Ridge (with a better salary and job title!), I recall almost immediately receiving a paper from Gene to referee for one of the journals he edited, with a cover letter saying that it was time for me to start giving back!

As with all of his students, Gene continued to be warmly supportive throughout my career and always had time to offer advice and counsel. This became especially valuable after I moved to an academic position at the University of Illinois at Urbana–Champaign in 1991, where coincidentally Gene had earned all three of his degrees, taking his PhD there in 1959. Gene seemed pleased by this symmetry, feeling that it was one way he could give back to his alma mater for its contribution to his own career. Indeed, Gene has said that the mutually supportive atmosphere he fostered at Stanford was based on his positive experience as a graduate student at Illinois during a pivotal time when many different disciplines were coming together to forge the new field of computer science.

Gene's grateful generosity toward Illinois took other concrete forms as well, first when he endowed the Hohn–Nash Scholarship for undergraduate students in scientific computing and later when he endowed the Paul and Cynthia Saylor Professorship in Computer Science. Gene's donation for the Saylor Professorship is especially telling, as it resulted from Google stock given to him by a grateful student whom Gene had generously helped with advice on an Internet search algorithm. Unlike most donors, Gene modestly declined to name the scholarship or professorship after himself, but rather chose to honor two of his teachers at Illinois (Franz Hohn and Jack Nash) and his long-standing friendship with Paul Saylor, an emeritus professor at Illinois, and his wife Cindy.

I was already on my way to the Bay Area for an Illinois alumni function when I heard that Gene was seriously ill with a potentially fatal illness. I headed straight for Stanford Hospital and visited him on what turned out to be the day before he died. He was obviously in precarious condition, and our chat was necessarily brief. Characteristically, his conversation was entirely about his pride in my achievements, without a word about his own condition. A couple of more recently graduated Stanford students also dropped by to see Gene while I was there, and he asked them to look in on his current house guest, a colleague from Germany if I recall correctly, and make sure that he was comfortable in view of Gene's inability to host him personally. Gene left this life the same way he had lived it, generously thinking of others to the very end.

Gene was born on leap day, February 29, 1932, and thus experienced a birthday only once every four years. Rather than feeling deprived, he found this calendrical accident amusing, and often joked about his age as measured in actual birthdays. Appropriately, his many friends and colleagues will gather around the globe to honor Gene's memory on February 29, 2008, which would have been his 19th birthday. For details, see For those wishing additional information about Gene's life and career, a list of relevant links can be found at

Michael Heath is Professor, Fulton Watson Copp Chair, Director of Computational Science and Engineering, and Interim Head of the Department of Computer Science at the University of Illinois at Urbana–Champaign.

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