Fast interval matrix multiplication

摘要

Several methods for the multiplication of point and/or interval matrices with interval result are discussed. Some are based on new 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 discussed and analyzed, 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 our methods are based on highly optimized BLAS3 routines. We discuss several possibilities to trade overestimation against computational effort. Numerical examples focussing in particular on applications using interval matrix multiplications are presented.