Fast interval matrix multiplication
Fast interval matrix multiplication
复制标题
快速区间矩阵乘法
作者：
S. Rump
讨论了点矩阵和/或区间矩阵与区间结果相乘的几种方法。有些是基于新的先验估计的误差的浮点矩阵产品。分析了包括所有舍入误差在内的高估量。特别地，讨论和分析了将下确界-上确界表示转换为中点-半径表示的算法，并证明了其中一种算法是最优的。所有的方法都比经典的方法快得多，因为几乎没有四舍五入模式的切换是必要的，因为我们的方法是基于高度优化的BLAS 3例程。我们讨论了几种可能性贸易高估计算工作。数值例子，特别是集中在使用区间矩阵乘法的应用。
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.