A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem

Abstract

We develop a parallel divide and conquer algorithm, by extension, for the generalized real symmetric definite tridiagonal eigenproblem. The algorithm employs techniques first proposed by Gu and Eisenstat to prevent loss of orthogonality in the computed eigenvectors for the modification algorithm. We examine numerical stability and adapt the insightful error analysis of Gu and Eisenstat to the arrow case. The algorithm incorporates an elegant zero finder with global monotone cubic convergence that has performed well in numerical experiments. A complete set of tested matlab routines implementing the algorithm is available on request from the authors.

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Document Details

Document Type
Technical Report
Publication Date
Dec 16, 1992
Accession Number
ADA262297

Entities

People

  • Carlos F. Borges
  • William B. Gragg

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Classification
  • Computations
  • Convergence
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Error Analysis
  • Errors
  • Inequalities
  • Intervals
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics
  • Orthogonality
  • Security

Readers

  • Computational Fluid Dynamics (CFD)
  • Linear Algebra