Analysis of the Symmetric Lanczos Process.

Abstract

The Lanczos algorithm is a powerful method for finding a few eigenvalues and eigenvectors of large sparse symmetric matrices. The quantities actually computed by the Lanczos algorithm diverge completely from their theoretical counterparts. In 1971 C. Paige showed that this instability merely resulted in the computation of multiple copies of eigenpairs of the matrix. This work presents and analyzes a new way of implementing the Lanczos algorithm which prevents the computation of redundant copies of eigenpairs and costs little more than simple Lanczos itself. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1978
Accession Number
ADA059999

Entities

People

  • David St. Clair Scott

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computational Complexity
  • Computations
  • Eigenvalues
  • Eigenvectors
  • Instability
  • Mathematical Analysis
  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra