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Matrix Computations
A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.
Matrix Computations
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Milestones in Matrix Computation
The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers is divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.
Matrices, Moments and Quadrature with Applications
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub
Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applica...
Recent Advances in Iterative Methods
This IMA Volume in Mathematics and its Applications RECENT ADVANCES IN ITERATIVE METHODS is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra. " Large systems of matrix equations arise frequently in applications and they have the prop erty that they are sparse and/or structured. The purpose of this workshop was to bring together researchers in numerical analysis and various ap plication areas to discuss where such problems arise and possible meth ods of solution. The last two days of the meeting were a celebration dedicated to Gene Golub on the occasion of his sixtieth birthday, with the program arranged by Jack Dongarra an...
Linear Algebra for Large Scale and Real-Time Applications
Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992
An Applied Mathematician’s Apology
In 1940 G. H. Hardy published A Mathematician's Apology, a meditation on mathematics by a leading pure mathematician. Eighty-two years later, An Applied Mathematician's Apology is a meditation and also a personal memoir by a philosophically inclined numerical analyst, one who has found great joy in his work but is puzzled by its relationship to the rest of mathematics.
Tensor Analysis
Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?
Advances in Information Retrieval
This book constitutes the refereed proceedings of the 28th European Conference on Information Retrieval Research, ECIR 2006, held in London, April 2006. The 37 revised full papers and 28 revised poster papers presented are organized in topical sections on formal models, document and query representation and text understanding, topic identification and news retrieval, clustering and classification, refinement and feedback, performance and peer-to-peer networks, Web search, cross-language retrieval, genomic IR, and much more.
