Cost-effective parallel preconditioner for network-based computing

A linear solver, the quasi-minimal residual, for a very large linear system is implemented for network-based computing. Network-based computing with a cluster of workstations or inexpensive personal computers has become an important and very successful technique. Network-based computing enables fast computation and resolves the shortage of storage with inexpensive computers on desks. A cluster of inexpensive computers offers aggregated computing power and sufficient storage to challenge large-scale problems. Assume that the total storage available in computers is just sufficient for solving the problem. This is often the case in real-world applications since the linear system is too large. Thus, any preconditioner which requires more storage than that available is excluded. Classical Jacobi, Gauss-Seidel, successive over relaxation and its variant, symmetric successive over relaxation, are considered. Performance of preconditioners is analyzed. The method is applied to a microwave oven linear system.