How to Make the Lanczos Algorithm Converge Slowly.

Abstract

The Paige style Lanczos algorithm is an iterative method for finding a few eigenvalues of large sparse symmetric matrices. Some beautiful relationships among the elements of the eigenvectors of a symmetric tridiagonal matrix are used to derive a perverse starting vector which delays convergence as long as possible. Why such slow convergence is never seen in practice is also examined. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 12, 1978
Accession Number
ADA058005

Entities

People

  • D. S. Scott

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Arithmetic
  • Convergence
  • Eigenvalues
  • Eigenvectors
  • Electronics
  • Equations
  • Error Analysis
  • Errors
  • Mathematics
  • Military Research
  • Notation
  • Polynomials
  • Residuals
  • Universities

Fields of Study

  • Mathematics

Readers

  • Linear Algebra