Misconvergence in the Lanczos Algorithm

Abstract

The Lanczos algorithm generates Ritz values in order to approximate eigenvalues. If some eigenvalues are clustered then a Ritz value may hover at a wrong value for a good number of steps. We study this phenomenon and focus on the point of discovery, the first step at which it is certain that there is a hidden eigenvalue in the vicinity of stabilized Ritz values. Both before and after this point the Ritz value behavior is routine - but for different eigenvalue configurations. The effective spread at step j is an interval guaranteed to contain all unknown eigenvalues. The notion of Ritz intervals leads to a computable counterpart to the exact theory.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1987
Accession Number
ADA206862

Entities

People

  • Beresford N. Parlett

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algebra
  • Algorithms
  • Applied Mathematics
  • Chebyshev Polynomials
  • Computations
  • Computer Science
  • Contracts
  • Eigenvalues
  • Errors
  • Intervals
  • Linear Algebra
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Polynomials
  • Theorems

Fields of Study

  • Mathematics

Readers

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