Author: Beresford N. Parlett
Publisher: SIAM
ISBN: 9781611971163
Category : Mathematics
Languages : en
Pages : 422
Get Book Here
Book Description
According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.
Author: Daniel Kressner
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
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 Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.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: David S. Watkins
Publisher: SIAM
ISBN: 9780898717808
Category : Mathematics
Languages : en
Pages : 452
Get Book Here
Book Description
The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
Author: Moody Chu
Publisher: Oxford University Press
ISBN: 0198566646
Category : Mathematics
Languages : en
Pages : 408
Get Book Here
Book Description
Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Author: Zhaojun Bai
Publisher: SIAM
ISBN: 0898714710
Category : Computers
Languages : en
Pages : 430
Get Book Here
Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Greg W. Anderson
Publisher: Cambridge University Press
ISBN: 0521194520
Category : Mathematics
Languages : en
Pages : 507
Get Book Here
Book Description
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Author: James W. Demmel
Publisher: SIAM
ISBN: 0898713897
Category : Mathematics
Languages : en
Pages : 426
Get Book Here
Book Description
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author: M.S. Moonen
Publisher: Springer Science & Business Media
ISBN: 9401581967
Category : Mathematics
Languages : en
Pages : 434
Get Book Here
Book Description
Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992
Author: J. Cullum
Publisher: Elsevier
ISBN: 0080872387
Category : Mathematics
Languages : en
Pages : 339
Get Book Here
Book Description
Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories:novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.
