Blockwise inversion and algorithms for inverting large partitioned matrices

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.