Singular value decomposition and least squares solutions
Author | : Gene H. Golub |
Publisher | : |
Total Pages | : 38 |
Release | : 1969 |
Genre | : |
ISBN | : |
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Author | : Gene H. Golub |
Publisher | : |
Total Pages | : 38 |
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 | : Gene Howard Golub (Mathematician, United States) |
Publisher | : |
Total Pages | : 76 |
Release | : 1969 |
Genre | : |
ISBN | : |
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 | : John L. Mather |
Publisher | : |
Total Pages | : |
Release | : 1986 |
Genre | : Signal processing |
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 | : 584 |
Release | : 2007-02-22 |
Genre | : Mathematics |
ISBN | : 9780199206810 |
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 | : James W. Demmel |
Publisher | : SIAM |
Total Pages | : 426 |
Release | : 1997-08-01 |
Genre | : Mathematics |
ISBN | : 0898713897 |
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author | : Sabine Van Huffel |
Publisher | : SIAM |
Total Pages | : 302 |
Release | : 1991-01-01 |
Genre | : Mathematics |
ISBN | : 0898712750 |
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.