Comparison Study and Operation Collapsing Issues for Serial Implementation of Square Matrix Multiplication Approach Suitable in High Performance Computing Environment

Abstract

Multiplication between two square matrices is one of the fundamental computational approach in the domain of mathematics and computer science where it is fully recognized as a fore most technique for several interdisciplinary domain and sub domains like linear algebra, graph theory, multidimensional graphics, cryptographic computation, convolution neural network, deep learning, digital signal processing, medical image processing, steganography, relativity theory, quantum computing and many others. In a high-performance computing environment computational complexity analysis of matrix multiplication algorithm ensures a powerful paradox that takes a massive data processing approach to the world where problem solution feasibility comes down in respect of operation and time. In our paper we have analyze different methods to multiply two square matrices (like 2×2 matrices) and their arithmetic complexity analysis in a asymptotic flavor along with operation collapsing issues through serial processing technique. We have analytically and experimentally explained and shown using MATLAB 9.3 simulator that fast matrix multiplication approach like Strassen and Winograd perform much better than conventional matrix multiplication algorithm especially for large amount of data.