The Introduction of Strassen's Algorithm and Application to 2^n Matrix Multiplication

Abstract

Abstract. In matrix calculation operations, especially the process of square matrix multiplication, as the order of the matrix increases, the level of accuracy required also increases. Manual calculation is prone to errors and takes a long time, especially for large order matrices. These problems can be overcome by using the Strassen algorithm. Strassen's algorithm views a matrix as a 2×2 matrix because it has four elements. Square matrix multiplication using the Strassen algorithm can be an alternative solution because the Strassen algorithm only contains seven multiplication processes. So, applying the Strassen algorithm to square matrix multiplication will be an alternative in accelerating the multiplication process, especially for matrices of a large order. This research discusses how the Strassen algorithm is formed and its application to the square matrix multiplication of order . Strassen's algorithm is obtained by transforming the elements of the product matrix C. Algebraic identity transformation is done by applying the properties that apply to the calculation operation without changing the original value. Using Strassen's Algorithm in the square matrix multiplication process can be an alternative in accelerating the multiplication process because Strassen's algorithm summarises the multiplication process into seven steps, compared to multiplication in general, which requires eight steps.