Accession Number : ADA118014

Title :   The Lanczos Algorithm for Solving Symmetric Linear Systems.

Descriptive Note : Final rept.,

Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS

Personal Author(s) : Simon,Horst D

PDF Url : ADA118014

Report Date : 20 Apr 1982

Pagination or Media Count : 109

Abstract : The Lanczos Algorithm is becoming accepted as a powerful tool for finding the eigenvalues and eigenvectors of large sparse matrices. This dissertation considers the application of the Lanczos algorithm to the solution of large sparse symmetric systems of linear equations. We analyze the symmetric Lanczos process with various reorthogonalization methods, and present a new implementation of the algorithm, which efficiently maintains orthogonality among the Lanczos vectors. This new algorithm is discussed in detail, compared to other methods, and tested with some numerical examples. (Author)

Descriptors :   *Algorithms, *Sparse matrix, *Linear systems, *Symmetry, Linear algebraic equations, Problem solving, Eigenvalues, Eigenvectors, Comparison, Orthogonality

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE