THE COMPUTATION OF BOUNDS FOR THE INVARIANT SUBSPACES OF A GENERAL MATRIX OPERATOR.

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)

Document Details

Document Type
Technical Report
Publication Date
May 26, 1967
Accession Number
AD0652921

Entities

People

  • James M. Varah

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Computations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Linear Algebra