An Adaptable Fast Matrix Multiplication Algorithm, Going Beyond the Myth of Decimal War

In this paper we present an adaptable fast matrix multiplication (AFMM) algorithm , for two nxn dense matrices which computes the product matrix with average complexity Tavg(n) = μ’d1d2n with the acknowledgement that the average count is obtained for addition as the basic operation rather than multiplication which is probably the unquestionable choice for basic operation in existing matrix multiplication algorithms. Here d1 and d2 are the densities (fraction of non-zero elements) of the pre and the post factor matrices only and μ’ is the expected value of the non zero elements of the post factor matrix. Remembering the fact that a single addition operation is much cheaper (however, this factor may differ from one machine to another) than a single multiplication operation, our algorithm finds the product matrix without using a single multiplication operation. The replacement of multiplications by additions has several significant and interesting aspects as it adds a non-determinism even to a problem which otherwise is considered to be deterministic! It can be argued that for inputs trivial as well as non trivial, AFMM algorithm can beat Strassen’s algorithm for matrix multiplication.