Preconditioning the matrix exponential operator with applications

Paul Castillo, Yousef Saad

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e Ay 0, using different approximations of the matrix A. These techniques are based on using generalized Kunge Kutta type methods. Preconditioned based on the sparsity structure of the matrix, such as diagonal, block diagonal, and least-squares tensor sum approximations arc presented. Numerical experiments are reported to compare the quality of the schemes introduced.

Original languageEnglish (US)
Pages (from-to)275-302
Number of pages28
JournalJournal of Scientific Computing
Volume13
Issue number3
DOIs
StatePublished - Sep 1998

Bibliographical note

Funding Information:
1 This work was supported by NSF under grant CCR-9618827 and by the Minnesota Super-computer Institute. 2 Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota 55455. 3 To whom correspondence should be addressed.

Keywords

  • Exponential operator
  • Generalized Runge Kutta methods
  • Preconditioner

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