An Efficient Parallel Algorithm of Modified Jacobi Approach for Sparse Linear System

Several parallel approaches have been developed to solve sparse linear system based on well-known memory saving schemes. To solve such a linear system, this article proposes a very simple parallel version of the modified Jacobi iterative method on Distributed Memory Architecture, using the well-known Compressed Sparse Row (CSR) storage format and Recursive Graph Bisection (RGB). The prime contribution of the present investigation is that the individual processors will not update its assigned variables any more, provided the previous iteration achieves smaller than the prescribed accuracy. Consequently, such processors will stop computation as well as communication with other processors to reduce both the computation and the communication time to a great extent. In fact, the use of such local stopping criteria ensures to achieve such overall system performance. The expected benefit of this algorithm is explained through the analytical results.