Java Multithreading based Parallel Preconditioned Generalized Conjugate Gradient type methods

A new class of Java multithreading based parallel approximate inverse preconditioning is introduced, for efficiently solving sparse arrow-type linear systems. The Parallel Explicit Preconditioned Biconjugate Conjugate Gradient - STAB method for shared memory systems is presented in order to examine the parallel behavior of this scheme using explicit approximate inverses as the suitable preconditioner. Design and implementation issues of Java´s multithreading techniques are also discussed. The performance in terms of speedups and parallel efficiencies of the method, using Java multithreading, is illustrated by solving sparse arrow-type linear systems. Static and dynamic workload scheduling systems implemented in Java and the results of their use are presented and discussed.