Fast and accurate algorithm for matrix multiplication using fused multiply-add

In this paper, we propose a new algorithm for high-precision matrix multiplication. When the accuracy of results from standard floating-point arithmetic is unsatisfactory, high-precision computation methods can be considered. Examples of such methods include pair arithmetic (PA) by Lange and Rump and double-word arithmetic (DW) by Bailey. In this study, we design a high-precision computation method that cleverly uses fused multiply-add (FMA) operations less costly than PA or DW. We also demonstrate its performance through numerical experiments.