Revisiting Strassen’s Matrix Multiplication for Multicore Systems

Abstract

Strassen’s matrix multiplication reduces the computational cost of multiplying matrices of size n × n from the O(n3) cost of a typical three-loop implementation to approximately O(n2.81). The reduction is made at the expense of additional operations of cost O(n2), and additional memory is needed for temporary results of recursive calls. The advantage of Strassen’s algorithm is therefore only apparent for larger matrices and it requires careful implementation. The increase in the speed of computational systems with several cores which share a common memory space also makes it more difficult for the algorithm to compete against highly optimized three-loop multiplications. This paper discusses various aspects which need to be addressed when designing Strassen multiplications for today’s multicore systems.