Random-walk interpretations of classical iteration methods

Jonathan Goodman; Neal Madras

doi:10.1016/0024-3795(93)00101-5

Random-walk interpretations of classical iteration methods

Jonathan Goodman, Neal Madras

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	61-79
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	216
DOIs	https://doi.org/10.1016/0024-3795(93)00101-5
State	Published - 1995

ASJC Scopus subject areas

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

Access to Document

10.1016/0024-3795(93)00101-5

Cite this

@article{1f3e55d7fa404134a4609b934334c1be,

title = "Random-walk interpretations of classical iteration methods",

abstract = "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.",

author = "Jonathan Goodman and Neal Madras",

year = "1995",

doi = "10.1016/0024-3795(93)00101-5",

language = "English (US)",

volume = "216",

pages = "61--79",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Random-walk interpretations of classical iteration methods

AU - Goodman, Jonathan

AU - Madras, Neal

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84868035045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868035045&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(93)00101-5

DO - 10.1016/0024-3795(93)00101-5

M3 - Article

AN - SCOPUS:84868035045

VL - 216

SP - 61

EP - 79

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Random-walk interpretations of classical iteration methods

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this