High performance stationary iterative methods

Iterative methods are well-established in the context of scientific computing. They solve a problem by finding successive approximations to the true solution starting from an initial guess. Iterative methods are preferred when dealing with large size problems, as direct methods would be prohibitively expensive. They are commonly used for solving polynomial systems, systems of linear equations, and partial differential equations. Iterative methods normally make heavy demands on computational resources, both in terms of computing power and data storage requirements, and are thus required to be partitioned and executed in parallel. However, their standard sequential order offers little opportunity for parallelism. Hence, it is necessary to re-order their execution in order to exploit the parallel computing power of the underlying computational resources.