Accurate Matrix Multiplication with Multiple Floating-point Numbers

Abstract—This paper is concerned with an accurate computation of matrix multiplication, where components of matrices are represented by summation of floating-point numbers. Recently, an accurate summation algorithm is de-veloped by the latter three of the authors. In this paper, it is specialized to dot product. Using this, a fast implementa-tion of accurate matrix multiplication is discussed. Finally, some numerical results are presented to confirm the effec-tiveness of the proposed algorithm. 1