ACCURATE EIGENVALUES OF A SYMMETRIC TRI-DIAGONAL MATRIX

Abstract

Having established tight bounds for the quotient of two different lub-norms of the same tri-diagonal matrix J, the author observes that these bounds could be of use in an error-analysis provided a suitable algorithm were found. Such an algorithm is exhibited, and its errors are thoroughly accounted for, including the effects of scaling, over/underflow and roundoff. A typical result is that, on a computer using rounded bloating point binary arithmetic, the biggest eigenvalue of J can be computed easily to within 2.5 units in its last place, and the smaller eigenvalues will suffer absolute errors which are no larger. These results are somewhat stronger than had been known before. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 22, 1966
Accession Number
AD0638796

Entities

People

  • W. Kahan

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Binary Arithmetic
  • Computations
  • Computer Science
  • Computers
  • Convex Sets
  • Eigenvalues
  • Error Analysis
  • Errors
  • Inequalities
  • Numbers
  • Numerical Analysis
  • Perturbations
  • Precision

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.