Accession Number : AD0652921
Title : THE COMPUTATION OF BOUNDS FOR THE INVARIANT SUBSPACES OF A GENERAL MATRIX OPERATOR.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
Personal Author(s) : Varah,James M.
Report Date : 26 MAY 1967
Pagination or Media Count : 246
Abstract : Let A be a general n x n complex matrix. We consider the problem of finding the invariant subspaces of A, i.e. solving AX = XM for X nonsingular and M block-diagonal. We first consider finding the eigensystem of A (i.e. M diagonal), assuming approximations to the eigenvalues are given. We show how to find approximate eigenvectors and rigorous machine bounds for the errors in the approximate eigensystem. Then we show how to find approximations and rigorous error bounds for higher-dimensional invariant subspaces of matrices which are close, in a sense we describe, to defective matrices, and for which poor results would be obtained for the eigensystem. Burroughs B5500 Extended Algol programs using these methods are also given. (Author)
Descriptors : (*MATRICES(MATHEMATICS), MATHEMATICS), PERTURBATION THEORY, THESES, COMPUTER PROGRAMS, ERRORS, TRANSFORMATIONS(MATHEMATICS), APPROXIMATION(MATHEMATICS), MATHEMATICAL ANALYSIS, THEORY
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE