The Use of Parallel Polynomial Preconditioners

This book mainly explores the use of polynomial preconditioners in iterative solvers for large-scale sparse linear systems Ax = b. It is well known that preconditioners can significantly improve the convergence of solvers, particularly when the coefficient matrix is ill-conditioned. Further, polynomial preconditioners have several advantages over other popular preconditioners - they may be implemented easily, they are highly parallel, and they are extremely agile. Due to the intrinsic disadvantages of polynomial methods (e.g., spectrum information is needed, poor stability of the large-degree polynomial preconditioning) and the limitation of computing technologies, the polynomial preconditioning technique was somehow ignored in the past ten years. Fortunately, at present, polynomial preconditioners are attracting more and more attention with the development of computer science.