The Use of Refined Error Bound When Updating Eigenvalues of Tridiagonals

Abstract

The Lanczos algorithm is used to compute some eigenvalues of a given symmetric matrix of large order. At each step of the Lanczos algorithm it is valuable to know which eigenvalues of the associated tridiagonal matrix have stabilized at eigenvalues of the given symmetric matrix. We present a robust algorithm which is fast (20j to 40j operation at j-th Lanczos step), uses about 30 words of extra storage, and has a fairly short program (approx 200 executable statements).

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1983
Accession Number
ADA134163

Entities

People

  • B. Nour-omid
  • Beresford N. Parlett

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Counter IED
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Computations
  • Computer Science
  • Computers
  • Eigenvalues
  • Eigenvectors
  • Electrical Engineering
  • Equations
  • Errors
  • Mathematics
  • Notation
  • Numbers
  • Precision
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Computational Linguistics
  • Linear Algebra