Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Volume 1, Theory

Front Cover
Society for Industrial and Applied Mathematics, Sep 1, 2002 - Computers - 268 pages
1 Review
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.

What people are saying - Write a review

We haven't found any reviews in the usual places.

Other editions - View all

References to this book

All Book Search results »

About the author (2002)

Cullum is a member of the Technical Staff of the Computer and Computational Sciences Division at Los Alamos National Laboratory.

Willoughby was a member of the Research Staff in the Mathematical Sciences Department in IBM Research from 1957-1991. He organized the first Symposium on Sparse Matrices in 1968.

Bibliographic information