Performance evaluation of multiple precision matrix multiplications using parallelized Strassen and Winograd algorithms

TL;DR

This paper evaluates the performance of parallelized Strassen and Winograd algorithms for multiple precision matrix multiplication, demonstrating significant speedups in dense matrix operations and LU decomposition in high-precision environments.

Contribution

It extends the effectiveness of parallelized Strassen and Winograd algorithms to double-double and quadruple-double precision environments, showing improved performance in matrix multiplication and LU decomposition.

Findings

Parallelized algorithms increase multiplication speed

Effective in double-double and quadruple-double precisions

Accelerates LU decomposition in high-precision settings

Abstract

It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision floating-point arithmetic environments such as the MPFR/GMP library. In this paper, we show that we can obtain the same effectiveness for double-double (DD) and quadruple-double (QD) environments supported by the QD library, and that parallelization can increase the speed of these multiple precision matrix multiplications. Finally, we demonstrate that our implemented parallelized Strassen and Winograd algorithms can increase the speed of parallelized LU decomposition.