Convergence of a parallel jacobi-type method

Abstract

A relaxed Jacobi-type iterative scheme is presented for solving linear algebraic systems. The method possesses a high level of parallelism and can be implemented on a multiprocessor system with or without synchronisation. The convergence region of the relaxation parameter is determined under the condition that the Jacobi iteration matrix possesses real eigenvalues. However, when the method is applied to consistently ordered systems, it is preferrable to let the parameter equal to unity and use Conjugate Gradient methods [3] to further increase the convergence rate.

Keywords:

• Parallel iterative algorithms
• Linear systems
• Relaxation techniques

Subject Classification:

• AMS(MOS): 65F10
• C.R: 5.14