Reduction of matrix products and their error bounds

A method is proposed for reducing the number of multiplies required for matrix-vector dot and matrix-matrix cross products. The technique requires the condition that k/spl ges/2 elements of the matrix be equal and results in k-1 less multiply operations for matrix-vector dot products. The savings are increased for matrix-matrix cross products. When all the elements of the matrix are unequal, the method can be extended to reduce the number of multiplies by k-1 with the artificial enforcement of k equal elements. The resulting error can be bounded for regular matrices. An example is submitted and discussed. The approach can be applied in conjunction with other matrix multiply reduction techniques and is useful in signal processing optimization for filtering, convolution and correlation using DSPs and RISCs.