Memory-Usage Advantageous Block Recursive Matrix Inverse
For practitioners needing to invert large matrices that do not fit in memory, this algorithm provides a feasible trade-off between memory and time.
The paper proposes a recursive block matrix inversion algorithm that reduces memory usage by computing one block of the inverse at a time, enabling inversion of matrices that would otherwise exceed memory limits at the cost of increased computational complexity.
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.