This award supports Professor Daniel Szyld of Temple University to collaborate in applied and computational mathematics with Professor Andreas Frommer of the Institute for Applied Mathematics of the University of Karlsruhe, Germany. The two researchers have worked on different aspects of the study of iterative methods for the efficient solution of linear and nonlinear algebraic systems of equations on both sequential and parallel computers. Frommer has worked extensively on linear and nonlinear asynchronous methods and on multisplitting methods. Szyld and his coauthors have worked on two-stage methods, including the tools needed for their analysis and computational experiments. Recently the two collaborators completed a study of two-stage iterative methods for H-matrices. In the proposed new work, they will extend this study to block two-stage methods and asynchronous (chaotic) parallel methods. They will look at both convergence properties as well as implementation details. This work relies heavily on the complementary expertise that each has developed in prior work. A central problem in many science and engineering applications is the solution of large linear systems of algebraic equations. The cooperating scientists will study theoretical, computational and algorithmic aspects of the solution of such systems and their applications. The project is likely to result in criteria to determine an optimal or near-optimal number of inner iterations to guarantee overall convergence and reduce parallel computing time.
