Accelerated Multiple Precision Matrix Multiplication using Strassen's Algorithm and Winograd's Variant

TL;DR

This paper introduces a novel approach to accelerate multiple precision matrix multiplication using Strassen's algorithm and Winograd's variant, demonstrating performance improvements and unique properties in applications like LU decomposition.

Contribution

It presents the first implementation of accelerated multiple precision matrix multiplication with these algorithms, applicable to matrices of any size.

Findings

Performance improvements in multiple precision matrix multiplication

Application to LU decomposition reveals special properties

Effective for matrices of arbitrary size

Abstract

The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as double-precision matrix multiplication by using these algorithms, no research to date has been undertaken to accelerate multiple precision matrix multiplication. In this paper, we propose a multiple precision matrix multiplication program for matrices of any size and test its performance. We also reveal special properties of our program through its application to LU decomposition.