The Complete Pivoting Conjecture for Gaussian Elimination is False

Volume 2, Issue 2
1992

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.