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

Many algorithms employing short recurrences have been developed 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. While this approach has merit in a sequential computing environment, it is even more valuable in a parallel environment. By combining global communications, the cost of three methods can be reduced to that of a single method.