Chebyshev Semi-Iterative Methods, Successive Over-Relaxation Iterative Methods, And Second-Order Richardson Iterative Methods, Parts I And Ii (With R. S. Varga)

Abstract

Abstract I was invited, in 1960 I believe, by Abe Taub at the University of Illinois, to a colloquium lecture there, and before the lecture, I was asked by Professor Taub what my current research was. I mentioned two areas, one being the use of Chebyshev polynomials in the theory of iterative methods in linear algebra. Taub mentioned then that he had a student (who turned out to be Gene Golub) working on similar ideas. What I learned later was that Taub told Gene that “if Varga publishes first, you will have to write a new thesis”. During that visit, I later met Gene, who was visibly shaken about all of this, and I suggested that we discuss this further over coffee. There was indeed overlap in our results, but Gene did things that I hadn’t done, and conversely. We then agreed to write a paper, in two parts, which appeared in Numerical Mathematics in 1961. This paper was surely better than either of us could have done alone, and it was quite a successful research paper, which was highly referenced. Adding to all of this is that Gene has often said that “Varga saved my life,” meaning that he didn’t have to write a second thesis! I have often been asked why Gene and I didn’t write more papers together. Sincerely, it would have been nice, but I wandered, as time went by, more into approximation theory and complex function theory, where my PhD thesis arose, and Gene had chosen other interesting areas in which to work. He had been a stellar figure in the area of numerical analysis, and this field owes him much for his deep and useful research results.