eCommons

 

How Accurate is Gaussian Elimination?

Other Titles

Abstract

J.H. Wilkinson put Gaussian elimination (GE) on a sound numerical footing in the 1960's when he showed that with partial pivoting the method is stable in the sense of yielding a small backward error. He also derived bounds proportional to the condition number κ(A) for the forward error xx^, where x^ is the computed solution to Ax=b. More recent work has furthered our understanding of GE, largely through the use of componentwise rather than normwise analysis. We survey what is known about the accuracy of GE in both the forward and backward error senses. Particular topics include: classes of matrix for which it is advantageous not to pivot; how to estimate or compute the backward error; iterative refinement in single precision; and how to compute efficiently a bound on the forward error. Key Words: Gaussian elimination, partial pivoting, rounding error analysis, backward error, forward error, condition number, iterative refinement in single precision, growth factor, componentwise bounds, condition estimator.

Journal / Series

Volume & Issue

Description

Sponsorship

Date Issued

1989-07

Publisher

Cornell University

Keywords

computer science; technical report

Location

Effective Date

Expiration Date

Sector

Employer

Union

Union Local

NAICS

Number of Workers

Committee Chair

Committee Co-Chair

Committee Member

Degree Discipline

Degree Name

Degree Level

Related Version

Related DOI

Related To

Related Part

Based on Related Item

Has Other Format(s)

Part of Related Item

Related To

Related Publication(s)

Link(s) to Related Publication(s)

References

Link(s) to Reference(s)

Previously Published As

http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR89-1024

Government Document

ISBN

ISMN

ISSN

Other Identifiers

Rights

Rights URI

Types

technical report

Accessibility Feature

Accessibility Hazard

Accessibility Summary

Link(s) to Catalog Record