Milestones in Matrix Computation. The Selected Works of Gene H. Golub with Commentaries
At the meeting in Moscow in June 2005, Gil Strang suggested that there should be a collection of Gene Golub’s work to highlight his many important contributions to numerical analysis. Three mathematicians: Raymond H. Chan, Chen Greif and Dianne P. O’Leary, were honoured to take this pleasant task, aimed for February 2007, the 75th anniversary of Gene’s birth. Twenty-one papers (chosen by Gene Golub) included in the book reveal a lot about his working style, creativity and quickness. His papers are divided into five groups (a majority of the papers are well-known so we will not mention names of co-authors).
“Gene Golub has been a driving force in development and analysis of iterative methods for solving large sparse linear systems,” begins Anne Greenbaum in her commentary to the first group of four papers (Iterative methods for linear systems). Two of the included papers deal with Chebyshev semi-iterative methods, SOR and Hermitian and Skew-Hermitian splittings methods. The other two papers deal with the generalized conjugate gradient method for non-symmetric systems and for numerical solutions of elliptic partial differential equations.
Five papers, collected in the second group, are related to various least square problems, including singular value decomposition, numerical methods for solving least squares problems and an analysis of the TLS problem. The commentary to the second part (Solution of least squares problems) has been written by Åke Björck.
Five papers in the third group (Matrix factorizations and applications) illustrate several different facets of the matrix factorization paradigm. The papers deal with calculating singular values, the simplex method using LU decomposition, methods for modifying matrix factorizations and computing angles between linear subspaces. The three papers of the fourth group (Orthogonal polynomials and quadrature) have, according to Walter Gautschi, a distinctly interdisciplinary character in the sense that classical analysis problems are recast in terms of, and successfully solved by, techniques of linear algebra and, vice versa, problems that have a linear algebra flavour are approached and solved using tools of classical analysis. The last group (Eigenvalue problems) is introduced by G. W. Stewart. The papers solve specific problems: a modified matrix eigenvalue problem, an ill-conditioned eigensystem and a computation of the Jordan canonical form, the block Lanczos method and a numerically stable reconstruction of a Jacobi matrix from spectral data. A list of publications, major awards, students of Gene Golub and his fascinating biography are included at the beginning of the book.