Data Splitting for Parallel Linear Algebra Monte Carlo Algorithms

Many scientific and engineering applications involve the inversion of large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the Monte Carlo methods depend only on the number of chains and the length of those chains as well as on the number of non-zero elements per row. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by parallel computing technologies such as Message passing Interface (MPI). In this paper we show how parallel Monte Carlo methods for computing the inverse of a matrix can be implemented by using data splitting to decrease the memory usage and to increase the applicability of the method.