Using Parallel Banded Linear System Solvers in Generalized Eigenvalue Problems

Abstract

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1993
Accession Number
ADA273994

Entities

People

  • Hong Zhang
  • William F. Moss

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Aeronautics
  • Algorithms
  • Computations
  • Computer Programs
  • Computers
  • Contracts
  • Differential Equations
  • Efficiency
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Equations
  • Linear Systems
  • Multiprocessors
  • Permutations
  • Structural Mechanics

Readers

  • Linear Algebra
  • Parallel and Distributed Computing.