The Lanczos Algorithm with Implicit Deflation.

Abstract

The simple Lanczos process is very effective for finding a few extreme eigenvalues of a large symmetric matrix along with the associated eigenvectors. Unfortunately the process computes redundant copies of the outermost eigenvectors and has to be used with some skill. In this paper it is shown how a modification called implicit deflation stifles the formation of duplicate eigenvectors without increasing the cost of a Lanczos step significantly. The degree of linear independence among the Lanczos vectors is controlled without the costly process of reorthogonalization. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 02, 1977
Accession Number
ADA057999

Entities

People

  • Beresford N. Parlett
  • D. S. Scott

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

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

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Linear Algebra