What Hadamard Missed,

Abstract

Consider the task of finding all the eigenvalues of a dense matrix. We show how Hadamard's procedure (1891) can be organized into Aitken's H-table (1925) and how the H-table may be transformed into Rutishauser's qd-array (1953) with the help of the Lanczos algorithm. We show how the qd algorithm can be interpreted as defining the LR algorithm (1958). Finally we show how the original qd algorithm may be transformed into the shifted differential qd algorithm dqds developed by Fernando and Parlett (1993/94). The Lanczos algorithm takes a dense matrix into tridiagonal form and then dqds is a fast and accurate procedure for extracting the eigenvalues.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1996
Accession Number
ADA310609

Entities

People

  • Beresford N. Parlett

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Arithmetic Units
  • Coefficients
  • Complex Variables
  • Computations
  • Eigenvalues
  • Mathematics
  • Meromorphic Functions
  • Polynomials
  • Precision
  • Rational Functions
  • Sequences
  • Theorems
  • Theses

Readers

  • Linear Algebra