Stability Analysis of the Fast Matrix Multiplication Algorithm

Abstract

This study focuses on the fast matrix multiplication algorithm. Numerical stability is the most crucial analysis for computation to obtain accurate results in scientifc research. Go through the timeline of fast matrix multiplication algorithms, and based on the current matrix multiplication algorithms, study the main idea of these algorithms, and analyze these algorithms’ stability in computation. The principal important part is using the forward error analysis to examine the matrix multiplication algorithm. Furthermore, simulate the stability of Strassen’s method and the Strassen-Winograd method by using C++ language.