Solving Linear Systems on Multiprocessors

Abstract

The purpose of the research was to study robust iterative methods for solving spare (block tridiagonal) nonsymmetric linear systems in a parallel computing environment. A new method was developed which uses block-row symmetric successive overrelaxation (SSOR) with conjugate gradient (CG) acceleration. The method is robust, with convergence assured even for poorly conditioned systems, and the method is easily implemented in a parallel environment. The method transforms a nonsymmetric system with an arbitrary eigenvalue distribution into a symmetric one with eigenvalue restricted to the interval (0,1). Research included testing of the algorithms on an Alliant FX/8 multiprocessor where it was demonstrated that the methods is very robust and performs better than standard existing methods.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1988
Accession Number
ADA200741

Entities

People

  • Ahmed H. Sameh

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computational Fluid Dynamics
  • Computations
  • Computers
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Environment
  • Equations
  • Iterations
  • Linear Systems
  • Mathematics
  • Multiprocessors
  • Numerical Analysis
  • Parallel Computing
  • Partial Differential Equations

Readers

  • Distributed Systems and Data Platform Development
  • Linear Algebra
  • Parallel and Distributed Computing.