Efficient Parallel Solution of Linear Systems with Hyperbolic Rotations.

Abstract

An algorithm based on hyperbolic rotations is presented for the solution of linear systems of equations, Ax = b, with symmetric positive definite coefficient matrix A. Forward elimination and backsubstitution are replaced by matrix vector multiplications, rendering the method most amenable to implementation on a variety of parallel and vector machines. The stability behaviour compares favourably with that of the best, known methods. The method can be simplified and formulated without square roots if A is also Toeplitz; a corresponding systolic architecture (in very large scale integrated circuits) for the resulting recurrence equations is more efficient than previously proposed pipelined Toeplitz system solvers. The hardware count becomes independent of the matrix size if its inverse is banded.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1984
Accession Number
ADA152355

Entities

People

  • I. C. F. Ipsen
  • J. M. Delosme

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Circuits
  • Coefficients
  • Elimination
  • Equations
  • Integrated Circuits
  • Large Scale Integrated Circuits
  • Linear Systems
  • Mathematics
  • Rotation
  • Square Roots

Readers

  • Computational Fluid Dynamics (CFD)
  • Computer Programming and Software Development.
  • Linear Algebra