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

TL;DR

This paper introduces an adaptable fast matrix multiplication algorithm that optimizes addition operations for dense matrices, challenging the traditional focus on multiplication as the primary computational cost.

Contribution

The paper presents a novel AFMM algorithm that emphasizes addition operations, offering a new perspective on optimizing matrix multiplication beyond the conventional multiplication-centric approach.

Findings

Achieves average complexity Tavg(n) = d1d2n3 for dense matrices.

Highlights the significance of addition operations in matrix multiplication efficiency.

Provides a new framework for developing adaptable matrix algorithms.

Abstract

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) = d1d2n3 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.