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.

翻译：分块矩阵结构在物理与工程应用中普遍存在。在计算此类分块矩阵的逆时，保留其分块结构具有多重优势。本文基于分块矩阵求逆技术，针对不同内存管理方式下的大型矩阵求逆问题，提出了相应算法。本文给出了一种将矩阵划分为大量子块并对其求逆的算法，该算法通过并行处理实现子块的求逆与乘法运算。该算法优化了内存管理，并实现了分块间中间乘法的高效计算方法。文中所述过程的开发程序以C语言实现，并行处理方法通过OpenMP应用编程接口实施。本文重点阐述了所开发算法的性能优势。