Generalization of error-free transformation for matrix multiplication and its application

Abstract

This paper is concerned with accurate numerical algorithms for matrix multiplication. Recently, an error-free transformation from a product of two floating-point matrices into an unevaluated sum of floating-point matrices has been developed by the authors. Combining this technique and accurate summation algorithms, new algorithms for accurate matrix multiplication could be investigated. In this paper, it is mentioned that the previous work is not the unique way to achieve an error-free transformation and the constraint of the error-free transformation is clarified. For the application, a new algorithm is developed reducing the number of matrix products compared to the previous algorithm.