Algorithmic bombardment for the iterative solution of linear systems : a poly-iteratve approach

Many algorithms exist for iteratively solving linear systems. Yet when the matrix is nonsymmetric or indefinite, or both, it is difficult to predict which method will perform best, or indeed, converge at all. Attempts have been made to classify the matrix properties for which a particular method will yield a satisfactory solution, but "luck" still plays large role. This report describes the implementation of a poly- iterative solver. Here we apply three algorithms simultaneously to the system, in the hope that at least one will converge to the solution. This approach has value in a sequential computing environment, yet it is in a parallel environment where it is even more valuable. Here we combine the global communication, effectively reducing these expensive operations to the cost of one method.