Algorithmic bombardment for the iterative solution of linear systems: A poly-iterative approach

Richard Barrett, Michael Berry, Jack Dongarra, Victor Eijkhout, Charles Romine

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

Many algorithms employing short recurrences have been developed for iteratively solving linear systems. Yet when the matrix is nonsymmetric or indefinite, or both, it is difficult to predict which method will perform best, or indeed, converge at all. Attempts have been made to classify the matrix properties for which a particular method will yield a satisfactory solution, but "luck" still plays large role. This report describes the implementation of a poly-iterative solver. Here we apply three algorithms simultaneously to the system, in the hope that at least one will converge to the solution. While this approach has merit in a sequential computing environment, it is even more valuable in a parallel environment. By combining global communications, the cost of three methods can be reduced to that of a single method.

Original languageEnglish
Pages (from-to)91-109
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume74
Issue number1-2
DOIs
StatePublished - Nov 5 1996

Keywords

  • Algorithmic bombardment
  • Iterative methods
  • Linear systems of equations
  • Poly-iterative approach

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