The Lanczos Algorithm for Solving Symmetric Linear Systems.

Abstract

The Lanczos Algorithm is becoming accepted as a powerful tool for finding the eigenvalues and eigenvectors of large sparse matrices. This dissertation considers the application of the Lanczos algorithm to the solution of large sparse symmetric systems of linear equations. We analyze the symmetric Lanczos process with various reorthogonalization methods, and present a new implementation of the algorithm, which efficiently maintains orthogonality among the Lanczos vectors. This new algorithm is discussed in detail, compared to other methods, and tested with some numerical examples. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 20, 1982
Accession Number
ADA118014

Entities

People

  • Horst D. Simon

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Differential Equations
  • Eigenvalues
  • Equations
  • Linear Algebra
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Real Variables
  • Sparse Matrix
  • Theses

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Theoretical Analysis.