Blockwise inversion and algorithms for inverting large partitioned matrices

TL;DR

This paper presents a parallel, memory-optimized algorithm for inverting large, partitioned matrices with block structures, leveraging parallel processing and efficient memory handling to improve performance in physics and engineering applications.

Contribution

It introduces a novel blockwise inversion algorithm that utilizes parallel processing and optimized memory management for large partitioned matrices.

Findings

Enhanced inversion speed with parallel processing

Efficient memory handling reduces computational overhead

Algorithm outperforms traditional methods in large matrix inversion

Abstract

Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using the blockwise matrix inversion technique, inversions of large matrices with different ways of memory handling are presented, in this article. An algorithm for performing inversion of a matrix which is partitioned into a large number of blocks is presented, in which inversions and multiplications involving the blocks are carried out with parallel processing. Optimized memory handling and efficient methods for intermediate multiplications among the partitioned blocks are implemented in this algorithm. The developed programs for the procedures discussed in this article are provided in C language and the parallel processing methodology is implemented using OpenMP application programming interface. The performance and the advantages of the developed algorithms are highlighted.