Random-walk interpretations of classical iteration methods

Jonathan Goodman, Neal Madras

Research output: Contribution to journalArticlepeer-review


We give a simple framework for computing relative convergence rates for relaxation methods with discrete Laplace operators (five point or nine point). This gives relations between the convergence rate for Jacobi, point Gauss Seidel, and various block relaxation strategies, essentially by inspection. The framework is a random walk interpretation of Jacobi relaxation that extends to these other relaxation methods.

Original languageEnglish (US)
Pages (from-to)61-79
Number of pages19
JournalLinear Algebra and Its Applications
StatePublished - 1995

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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