Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube.

Abstract

This paper describes implementations of Cuppen's method, bisection, and multisection for the computation of all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory hypercube multiprocessor. Numerical results and timings for Intel's iPSC are presented. Cuppen's method is the most accurate of the three. Near maximal speedups are demonstrated for Cuppen's method when little deflation occurs at intermediate steps, but speedups are significantly reduced when deflation leads to processor load imbalance. Bisection with inverse iteration is seen experimentally to be the fastest method sequentially and in parallel. The independent tasks comprising this approach lead to high parallel efficiency. The relative expected performance of parallel multisection is shown analytically to be problem dependent with arithmetic inefficiency arising in a wide class of problems. Moderate speedups are observed experimentally.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1987
Accession Number
ADA193905

Entities

People

  • Elizabeth R. Jessup
  • Ilse C. Ipsen

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Arrays
  • Computations
  • Computer Science
  • Computers
  • Data Transmission
  • Digital Communications
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Floating Point Operations
  • Operating Systems
  • Parallel Computing
  • Precision
  • Two Dimensional
  • Workload

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Parallel and Distributed Computing.