G. W. Stewart -- Biography of G. W. Stewart -- Publications, Honors, and Students -- Commentaries -- to the Commentaries -- Matrix Decompositions: Linpack and Beyond -- Updating and Downdating Matrix Decompositions -- Least Squares, Projections, and Pseudoinverses -- The Eigenproblem and Invariant Subspaces: Perturbation Theory -- The SVD, Eigenproblem, and Invariant Subspaces: Algorithms -- The Generalized Eigenproblem -- Krylov Subspace Methods for the Eigenproblem -- Other Contributions -- Reprints -- Papers on Matrix Decompositions -- Papers on Updating and Downdating Matrix Decompositions -- Papers on Least Squares, Projections, and Generalized Inverses -- Papers on the Eigenproblem and Invariant Subspaces: Perturbation Theory -- Papers on the SVD, Eigenproblem and Invariant Subspaces: Algorithms -- Papers on the Generalized Eigenproblem -- Papers on Krylov Subspace Methods for the Eigenproblem.

Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. It is widely accepted that Stewart is the successor to James Wilkinson, the first giant in the field, taking up the perturbation theory research that Wilkinson so ably began and using it as a foundation for algorithmic insights. Stewart’s results on rounding error in numerical computations provided basic understanding of floating-point computation. His results on perturbation of eigensystems, pseudo-inverses, least-squares problems, and matrix factorizations are fundamental to numerical practice today. His algorithms for the singular value decomposition, updating and downdating matrix factorizations, and the eigenproblem broke new ground and are still widely used in an increasing number of applications. Stewart’s papers, widely cited, are characterized by elegance in theorems and algorithms and clear, concise, and beautiful exposition. His six popular textbooks are excellent sources of knowledge and history. Stewart is a member of the National Academy of Engineering and has received numerous additional honors, including the Bauer Prize. Key features of this volume include: * Forty-four of Stewart’s most influential research papers in two subject areas: matrix algorithms and rounding and perturbation theory * A biography of Stewart * A complete list of Stewart’s publications, students, and honors * Selected photographs * Commentaries on Stewart’s works in collaboration with leading experts in the field G.W. Stewart: Selected Works with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics.