Memory-Usage Advantageous Block Recursive Matrix Inverse

TL;DR

This paper introduces a recursive block matrix inversion algorithm that reduces memory usage at the cost of increased computation, enabling inversion of very large matrices on limited-memory systems.

Contribution

A novel recursive algorithm for block matrix inversion that minimizes memory footprint by computing one block at a time, suitable for large matrices exceeding memory capacity.

Findings

Enables inversion of large matrices with limited memory

Increases computational complexity but reduces memory requirements

Successfully tested on matrices exceeding traditional memory limits

Abstract

The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider exchanging less memory usage for more processing time in order to enable the computation of the inverse which otherwise would be prohibitive. We propose a new algorithm to compute the inverse of block partitioned matrices with a reduced memory footprint. The algorithm works recursively to invert one block of a $k \times k$ block matrix $M$, with $k \geq 2$, based on the successive splitting of $M$. It computes one block of the inverse at a time, in order to limit memory usage during the entire processing. Experimental results show that, despite increasing computational complexity, matrices that otherwise would exceed the memory-usage limit can be inverted using this technique.