Residual Bounds on Approximate Eigensystems of Nonnormal Matrices,

Abstract

This paper is concerned with the following question and its ramifications. The goal is to compute some or all of the eigenvalues of a square matrix B which is not symmetric. There is on hand an approximate column eigenvector x, an approximate row eigenvector y*, and a number gamma. In addition someone has computed the norms of their residual vectors, abs. val r and abs. val. s*, where r = Bx-x gamma, s* = y*B-gamma y*. It turns out that abs. val. r/abs. val.x < or = abs. val. (.00001 B) and abs. val. s*/abs. val. y* < or = abs. val. (.00001 B1). How good is gamma as an approximate eigenvalue of B?

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Document Details

Document Type
Technical Report
Publication Date
Sep 05, 1980
Accession Number
ADA092577

Entities

People

  • Beresford N. Parlett
  • E. Jiang

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Complex Numbers
  • Computations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Error Analysis
  • Errors
  • New York
  • Notation
  • Numbers
  • Perturbation Theory
  • Perturbations
  • Residuals
  • Spectra
  • Square Roots
  • Theorems

Readers

  • Auditory Neuroscience/Auditory Physiology.
  • Linear Algebra