The Complete Pivoting Conjecture for Gaussian Elimination Is False -- from Wolfram Library Archive

Title

The Complete Pivoting Conjecture for Gaussian Elimination Is False

Author

A. Edelman

Journal / Anthology

The Mathematica Journal

Year:

1992

Volume:

Issue:

Page range:

58-61

Description

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.

Subject

Mathematics > Algebra > Linear Algebra

URL

http://www.mathematica-journal.com/issue/v2i2/

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