An algorithm for automatic round-off error analysis in discrete linear transforms

Abstract

The discrete linear transforms implemented on computers require a very great number of computations. The round-off errors inherent in the floating-point arithmetic of the computer generate errors in the results which may be fairly large. In this paper we propose an algorithm based on the La Porte-Vignes Perturbation Method which is able to automatically analyze the round-off error in any discrete linear transform. Furthermore, this algorithm supplies the local accuracy in any discrete transform in the case of experimental data (data errors and round-off errors).