FASTER NUMERICAL ALGORITHMS VIA EXCEPTION HANDLING

An attractive paradigm for building fast numerical algorithms is the f ollowing: 1) try a fast but occasionally unstable algorithm, 2) test t he accuracy of the computed answer, and 3) recompute the answer slowly and accurately in the unlikely event it is necessary. This is especia lly attractive on parallel machines where the fastest algorithms may b e less stable than the best serial algorithms. Since unstable algorith ms can overflow or cause other exceptions, exception handling is neede d to implement this paradigm safely. To implement it efficiently, exce ption handling cannot be too slow. We illustrate this paradigm with nu merical linear algebra algorithms from the LAPACK library.