Determining the Effects of Cross-over Point on the Running Time of Strassen Matrix Multiplication Algorithm

Abstract

This paper studies Strassen’s algorithms for fast multiplication of two finite dimensional matrices. However, one pertinent issue that has deterred Strassen’s scheme from been considered for practical usage is determining the cross-over point. In this light, large matrices with different sizes were randomly generated on which Strassen and conventional matrix multiplication algorithms were implemented in MATLAB R2008b. Two MATLAB built-in functions nextpow2 and pow2 were used for implementing padding techniques to ensure that the matrices are to the power of two. Three different experiments were carried out using five, four and three levels of recursion (divide and conquer algorithm) respectively to determine the suitable cut-off point  which were used to evaluate the optimal running time for Strassen’s algorithm. For each experiment, eight finite dimensional square matrices of real numbers were generated and iteratively multiplied. The experiment reveals that the cut-off point with five level of recursion optimized the Strassens time.