Fast interval matrix multiplication
The author discusses various methods for the multiplication of point and/or interval matrices with interval result. Some are based on new a priori estimates of the error of floating-point matrix products. The amount of overestimation including all rounding errors is analyzed. In particular, algorithms for conversion of infimum-supremum to midpoint-radius representation are studied, one of which is proved to be optimal. All methods are much faster than the classical method because almost no switch of the rounding mode is necessary, and because the methods are based on highly optimized BLAS3 routines. Several possibilities are discussed to trade overestimation against computational effort. Numerical examples are presented focussing in particular on applications using interval matrix multiplications.
scientific article; zbMATH DE number 6085769
scientific article