[PDF] Numerical Methods In Matrix Computations eBook

Author : Åke Björck
Publisher : Springer
Page : 812 pages
File Size : 10,71 MB
Release : 2014-10-07
Category : Mathematics
ISBN : 3319050893

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Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Author : Ake Bjorck
Publisher : SIAM
Page : 425 pages
File Size : 26,12 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 9781611971484

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The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 135 pages
File Size : 30,40 MB
Release : 2009-07-23
Category : Mathematics
ISBN : 0898716764

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Matrix analysis presented in the context of numerical computation at a basic level.

Author : Yousef Saad
Publisher : SIAM
Page : 292 pages
File Size : 47,52 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 9781611970739

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Author : Thomas F. Coleman
Publisher : SIAM
Page : 271 pages
File Size : 49,56 MB
Release : 1988-01-01
Category : Mathematics
ISBN : 9781611971040

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Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.

Author : Gene H. Golub
Publisher : JHU Press
Page : 734 pages
File Size : 30,64 MB
Release : 1996-10-15
Category : Mathematics
ISBN : 9780801854149

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Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Author : Zhong-Zhi Bai
Publisher : SIAM
Page : 496 pages
File Size : 43,76 MB
Release : 2021-09-09
Category : Mathematics
ISBN : 1611976634

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This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

Author : Germund Dahlquist
Publisher : SIAM
Page : 741 pages
File Size : 50,48 MB
Release : 2008-09-04
Category : Mathematics
ISBN : 0898716446

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This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Author : K. Gallivan
Publisher : SIAM
Page : 207 pages
File Size : 49,53 MB
Release : 1990-01-01
Category : Mathematics
ISBN : 9781611971705

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Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.