Lanczos Algorithms for Large Symmetric Eigenvalue Computations

Ralph A. Willoughby Jane K. Cullum

ISBN 10: 0817630589 / ISBN 13: 9780817630584

Published by Springer, 1984

About this Item

1st Edition.

Seller Inventory # 2648003508

Bibliographic Details

• Title: Lanczos Algorithms for Large Symmetric Eigenvalue Computations
• Publisher: Springer
• Publication Date: 1984
• Language: English
• ISBN 10: 0817630589
• ISBN 13: 9780817630584
• Binding: Hardcover
• Condition: New

About this title

Synopsis

First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book deals with 'symmetric' problems. However, in this book, 'symmetric' also encompasses numerical procedures for computing singular values and vectors of real rectangular matrices and numerical procedures for computing eigenelements of nondefective complex symmetric matrices. Although preserving orthogonality has been the golden rule in linear algebra, most of the algorithms in this book conform to that rule only locally, resulting in markedly reduced memory requirements. Additionally, most of the algorithms discussed separate the eigenvalue (singular value) computations from the corresponding eigenvector (singular vector) computations. This separation prevents losses in accuracy that can occur in methods which, in order to be able to compute further into the spectrum, use successive implicit deflation by computed eigenvector or singular vector approximations.