Handbook Series Linear Algebra
Author | : Gene Howard Golub (Mathematician, United States) |
Publisher | : |
Total Pages | : 76 |
Release | : 1969 |
Genre | : |
ISBN | : |
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Author | : Gene Howard Golub (Mathematician, United States) |
Publisher | : |
Total Pages | : 76 |
Release | : 1969 |
Genre | : |
ISBN | : |
Author | : G. H. Golub |
Publisher | : |
Total Pages | : 42 |
Release | : 1969 |
Genre | : Algebras, Linear |
ISBN | : |
Two Algol procedures are given which are useful in linear least squares problems. The first procedure computes the singular value decomposition by first reducing the rectangular matrix A to a bidiagonal matrix, and then computing the singular values of the bidiagonal matrix by a variant of the QR algorithm. The second procedure yields the components for the linear least squares solution when it is desirable to determine a vector X tilde for which norm (Ax-b) sub 2 = min. (Author).
Author | : John H. Wilkinson |
Publisher | : Springer Science & Business Media |
Total Pages | : 450 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 3642869408 |
The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.
Author | : Charles L. Lawson |
Publisher | : SIAM |
Total Pages | : 348 |
Release | : 1995-12-01 |
Genre | : Mathematics |
ISBN | : 0898713560 |
This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.
Author | : Leslie Hogben |
Publisher | : CRC Press |
Total Pages | : 1402 |
Release | : 2006-11-02 |
Genre | : Mathematics |
ISBN | : 1420010573 |
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl
Author | : Eric Carlen |
Publisher | : Macmillan |
Total Pages | : 360 |
Release | : 2007-04-13 |
Genre | : Mathematics |
ISBN | : 9781429204286 |
Author | : Gene H. Golub |
Publisher | : |
Total Pages | : 38 |
Release | : 1969 |
Genre | : |
ISBN | : |
Author | : James Bisgard |
Publisher | : American Mathematical Soc. |
Total Pages | : 217 |
Release | : 2020-10-19 |
Genre | : Education |
ISBN | : 1470463326 |
This book provides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book: determining the subspace that “best” approximates a given set (dimension reduction of a data set); finding the “best” lower rank approximation of a given matrix (compression and general approximation problems); the Moore-Penrose pseudo-inverse (relevant to solving least squares problems); and the orthogonal Procrustes problem (finding the orthogonal transformation that most closely transforms a given collection to a given configuration), as well as its orientation-preserving version. The point of view throughout is analytic. Readers are assumed to have had a rigorous introduction to sequences and continuity. These are generalized and applied to linear algebraic ideas. Along the way to the SVD, several important results relevant to a wide variety of fields (including random matrices and spectral graph theory) are explored: the Spectral Theorem; minimax characterizations of eigenvalues; and eigenvalue inequalities. By combining analytic and linear algebraic ideas, readers see seemingly disparate areas interacting in beautiful and applicable ways.
Author | : Raymond Chan |
Publisher | : OUP Oxford |
Total Pages | : 581 |
Release | : 2007-02-22 |
Genre | : Mathematics |
ISBN | : 0191525774 |
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.
Author | : Åke Björck |
Publisher | : SIAM |
Total Pages | : 509 |
Release | : 2024-07-05 |
Genre | : Mathematics |
ISBN | : 1611977959 |
The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to-date treatment of direct and iterative methods for solving different types of least squares problems and for computing the singular value decomposition. It also is unique because it covers generalized, constrained, and nonlinear least squares problems as well as partial least squares and regularization methods for discrete ill-posed problems. The bibliography of over 1,100 historical and recent references provides a comprehensive survey of past and present research in the field. This book will be of interest to graduate students and researchers in applied mathematics and to researchers working with numerical linear algebra applications.