By Raymond Chan, Chen Greif, Dianne O'Leary
The textual content offers and discusses probably the most influential papers in Matrix Computation authored via Gene H. Golub, one of many founding fathers of the sector. the gathering of 21 papers in divided into 5 major parts: iterative equipment for linear platforms, answer of least squares difficulties, matrix factorizations and purposes, orthogonal polynomials and quadrature, and eigenvalue difficulties an commentaries for every region are supplied through prime specialists: Anne Greenbaum, Ake Bjorkc, Nicholas Higham, Walter Gautschi, and G.W (Pete) Stewart. reviews on every one paper also are supplied by way of the unique authors, offering the reader with ancient info on how the paper got here to be written and below what conditions the collaboration was once undertaken. together with a short biography and facsimiles of the unique papers, this article will be of significant curiosity to scholars and researchers in numerical research and medical computation.
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Extra info for Milestones in Matrix Computation: The Selected Works of Gene H. Golub with Commentaries
J162] (with Oren E. Livne), Scaling by binormalization, Numer. Algorithms 35, 97-120 (2004). [J163] (with R. Vandebril, M. Barel, and N. Mastronardi), A bibliography on semiseparable matrices, Calcolo 43, 249-270 (2005). [J164] (with G. Boutry, M. Elad, and P. Milanfar), The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach, SIAM J. Matrix Anal. Appl. 27, 582-601 (2005). 28 Publications of Gene H. Golub [J165] (with Y. Tsaig, M. Elad, P. Milanfar), Variable projection for near-optimal filtering in low bit-rate block coders, IEEE Trans.
C50] (with Shivkumar Chandrasekaran, Ming Gu, Ali. H. Sayed)Efficient algorithms for least squares type problems with bounded uncertainties, in Recent Advances in Total Least Squares Techniques and Errors-in- Variables Modeling, Sabine Van Huffel (ed), SIAM, 171-182 (1997). [C51] (with Urs von Matt), Tikhonov regularization for large scale problems, in Scientific Computing, Gene Howard Golub(ed), Springer, 3-26 (1997). [C52] (with Knut Solna and Paul van Dooren), Computing the SVD of a general matrix product/quotient, SIAM J.
We review five of his seminal papers in this field. Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II, by Golub and Varga  This paper is probably less well-known today than it should be. In it the authors show the remarkable similarity between the Chebyshev semi-iterative method, the successive overrelaxation (SOR) method applied to an expanded matrix equation, and the second-order Richardson iterative method.