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# 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

# Report Date:

## 1967-05-26

# Pagination or Media Count:

##
246.0

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#