• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1463-1475
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• 2011

This paper proposes a new generalized iterative method (SSOR-like method) for solving augmented system. A functional equation relating two involved parameters is obtained, and some convergence conditions for this method are derived. This paper generalizes some foregone results. Numerical examples show that, this method is efficient by suitable choices of the involved parameters.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.593-602
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• 2012

In this paper, we first introduce a special type of multisplitting method with different weighting scheme, and then we provide convergence results of multisplitting methods with different weighting schemes corresponding to both the AOR-like multisplitting and the SSOR-like multisplitting.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.305-316
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• 2003

Recently, an iterative algorithm for finding the interior eigenvalues of a definite matrix by CG-type method has been proposed. This method compares to the inverse power method. The given matrices A, and B are assumed to be large and sparse, and SPD( Symmetric Positive Definite) The CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for smallest eigenvalue. Also, it is very amenable to parallel computations, like the CG method for the linear systems. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. But for parallel computations we need to find an efficient parallel preconditioner. Our candidates we ILU(0) in the wave-front order, ILU(0) in the multi-coloring order, Point-SSOR(Symmetric Successive Overrelaxation), and Multi-Color Block SSOR preconditioner. Wavefront order is a simple way to increase parallelism in the natural order, and Multi-coloring realizes a parallelism of order(N), where N is the order of the matrix. Another choice is the Multi-Color Block SSOR(Symmetric Successive OverRelaxation) preconditioning. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test problem was drawn from the discretizations of partial differential equations by finite difference methods. The results show that for small number of processors Multi-Color ILU(0) has the best performance, while for large number of processors Multi-Color Block SSOR performs the best.