Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications (Q662894)

The authors develop a fast and accurate method to evaluate matrix products error free. An error free splitting of floating point numbers with regards to number product is generalized to accurate dot products of vectors and error free matrix products. Floating point numbers, vectors and matrices are split into a sum of numbers, vectors and matrices, respectively, with a limited small number of nonzero leading bits and their products are expressed as non-evaluated sums of accurate floating point products until the matrix product stage is reached. There 3rd level BLAS are used to give fast and accurate matrix products. This method uses the more memory the deeper (shorter nonzero bit length) the splittings become.