An Analysis of Lanczos Algorithms for Symmetric Matrices,

Abstract

The Lanczos algorithm is presented as a way of generating bases for a sequence of Krylov subspaces. Explicit expressions are given for the departure of the bases from orthogonality. These relations enable one to comprehend the behavior of the algorithm in practice with a minimum of conventional error analysis. In particular this approach sheds light on the central, and difficult problem of ascertaining the right moment to stop the algorithm. Reorthogonalization and block versions are also examined.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1974
Accession Number
ADA006361

Entities

People

  • Beresford N. Parlett
  • W. Kahan

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Error Analysis
  • Errors
  • Mathematics
  • Orthogonality

Readers

  • Linear Algebra
  • Systems Analysis and Design