By James E. Gentle
John L. Greenstadt, 1924-2022. Photo courtesy of Eliza Greenstadt.
John L. Greenstadt, an applied mathematician who worked in the field for over 70 years, passed away on October 17, 2022, shortly after his 98th birthday. He was one of the few remaining members of the early generation of numerical analysts who were the first to enjoy widespread access to digital computers — albeit behind the glass walls of a “computer room.” Richard W. Hamming, Alston S. Householder, Gene Golub, and Michael Powell were also among these pioneers.
John was born on October 8, 1924, in New York City. After serving in the U.S. Army during World War II (he worked on flight and artillery engineering), John earned a B.A. in physics from Brooklyn College in 1944. In 1953, he received a Ph.D. in mathematical physics from Yale University under the mentorship of Lars Onsager, who later won the 1968 Nobel Prize in Chemistry. John joined IBM in 1952 and retained his role as a staff scientist for 33 years.
According to Google Scholar, one of John’s earliest papers is “A Method for Finding Roots of Arbitrary Matrices”, which describes a sequence of unitary transformations to triangularize a square matrix [1]. Doing so enables computation of the eigenvalues of a non-normal matrix (which cannot be diagonalized). Variations of this method are still in use today, but the article’s reference to numerical software is also historically interesting. It briefly describes “a program written in the “Speedcoding” floating-point system for the IBM 701” and offers timing results that one can normalize with the knowledge that “the average time per multiplication or addition in this system is 4 milliseconds”!
John later wrote an important paper titled “On the Relative Efficiencies of Gradient Methods,” which addressed the lack of positive definiteness in a sequence of Hessians in Newton descents [2]. Mathematicians still employ the basic ideas of his quasi-Newton method, which is sometimes called the “Greenstadt modification.” In a 2000 article in honor of William C. Davidon, John surveyed the development of what came to be known as the “variational approach” in optimization [3]. This paper contains a statement that provides an interesting perspective on the times: “In 1971, while I was a visitor at the University of Dundee for six months, I did not have access to a computer, and so was not able to carry on with my work on Cell Discretization in which I was then involved.”
During his time at IBM, John was active in the SHARE program, which was an important distribution outlet for numerical software in the 1950s and 1960s. After leaving IBM in 1985, he continued his research endeavors at the University of Dundee and the University of Cambridge before retiring in Mountain View, Calif. Even in retirement, he kept working on numerical analysis problems.
John will be remembered by his children, his nieces and nephews, and all who knew him for his incisive wit, playful humor, and prodigious knowledge of a variety of subjects from politics and history to art and music. He will be sorely missed.
References
[1] Greenstadt, J. (1955). A method for finding roots of arbitrary matrices. Math. Tables Other Aids Comput., 9(50), 47-52.
[2] Greenstadt, J. (1967). On the relative efficiencies of gradient methods. Math. Comput., 21(99), 360-367.
[3] Greenstadt, J. (2000). Reminiscences on the development of the variational approach to Davidon’s variable-metric method. Math. Program., 87, 265-280.
James E. Gentle is University Professor Emeritus of Computational Statistics at George Mason University. He is the author of several books and papers in statistics.