The Complete Pivoting Conjecture for Gaussian Elimination is False
Alan S. Edelman · eScholarship (California Digital Library) · 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.