A method of ultra-large-scale matrix inversion using block recursion

Abstract

Ultra-large-scale matrix inversion has been applied as the fundamental operation of numerous domains, owing to the growth of big data and matrix applications. Using cryptography as an example, the solution of ultra-large-scale linear equations over finite fields is important in many cryptanalysis schemes. However, inverting matrices of extremely high order, such as in millions, is challenging; nonetheless, the need has become increasingly urgent. Hence, we propose a parallel distributed block recursive computing method that can process matrices at a significantly increased scale, based on Strassen’s method; furthermore, we describe the related well-designed algorithm herein. Additionally, the experimental results based on comparison show the efficiency and the superiority of our method. Using our method, up to 140,000 dimensions can be processed in a supercomputing center.