The Impact of Parallel Architectures on the Solution of Eigenvalue Problems.

Abstract

The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. A simple model will be given to analyse the complexity of parallel algorithms on several representative multiprocessor systems: a linear processor array (or ring), a two-dimensional processor grid and the hypercube. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on the above architectures will be described, as well as parallel implementations of the following classes of eigenvalue methods: QR, bisection, divide-and-conquer, and Lanczos algorithm.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1985
Accession Number
ADA163187

Entities

People

  • Ilse C. F. Ipsen
  • Youcef Saad

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Computations
  • Eigenvalues
  • Linear Algebra
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Multiprocessors
  • Parallel Computing
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Parallel and Distributed Computing.
  • Theoretical Analysis.