The Mathematica Journal

Search

About the Journal
Current Issue
Editorial Policy
Submissions
Back Issues
Contact Information

index.html

The Complete Pivoting Conjecture for Gaussian Elimination is False

Volume 2, Issue 2
1992
Alan Edelman, University of California at Berkeley and Lawrence Berkeley Laboratory
 

A famous conjecture concerning Gaussian Elimination was recently "settled" as false, by a counterexample found on a Cray supercomputer. Mathematica did not yield the same conclusion when given identical data, reminding us of the care needed when proving mathematical statements using rounded arithmetic. Indeed, the conjecture is false, but a proper counterexample requires modifications of the data. In this note, we provide proper counterexamples by modifying numbers computed in rounded arithmetic by Nick Gould on a Cray.

     
About Mathematica 
© Wolfram Media, Inc. All rights reserved.