A new Walk on Equations Monte Carlo method for solving systems of linear algebraic equations

A new Walk on Equations (WE) Monte Carlo algorithm for solving systems of linear algebraic (LA) equations is proposed and studied. This algorithm relies on a non-discounted sum of an absorbed random walk. It can be applied for either real or complex matrices. Several techniques like simultaneous scoring or the sequential Monte Carlo method are applied to improve the basic algorithm. Numerical tests are performed on examples with matrices of different size and on systems coming from various applications. Comparisons with standard deterministic or Monte Carlo algorithms are also done.