On Distributed Solution for Simultaneous Linear Symmetric Systems

Cholesky Decomposition is the primary approach which is used to solve Symmetric and Positive Definite (SPD) systems but is inherently iterative making it very difficult to parallelize as calculations at each partition require elements from other partitions. In this paper, we present two distributed block-recursive approaches to solve large SPD systems - the symmetric version of the state-of-the-art Strassen's algorithm and Cholesky based inversion algorithm. We show experimentally that both the approaches have good scalability and Cholesky based approach is more efficient as it uses fewer matrix multiplications in each recursion level than Strassen based algorithm.