Abstract
Non-stationary Parallel Multisplitting Two-Stage Iterative Methods with Self-AdaptiveWeighting Schemes
Highlights
To solve large sparse linear system of equations on multiprocessor systems, Ax = b, A = ∈ Rn×n nonsingular and b ∈ Rn . (1)O’Leary and White [14] first proposed parallel methods based on multisplitting of matrices in 1985, after this, combing with two-stage iterative methods, the multisplitting two-stage iterative methods [15] were proposed, where several basic convergence results were found
Many authors studied the methods for the case that A is an M-matrix, an H-matrix and a symmetric positive definite matrix
None has ever studied that how to choose optimal weighting matrices for the parallel multisplitting two-stage iterative algorithms, we will discuss this problem in the paper
Summary
When A is an M-matrix or an H-matrix, many parallel multisplitting two-stage iterative methods (see [3, 5, 6, 12, 15, 17]) were presented, and the weighting matrices Ei, i = 1, 2, · · · , m were generalized (see [1, 11]). Wang [23] has presented modified parallel multisplitting iterative methods by optimizing the weighting matrices based on the sparsity of the coefficient matrix A. None has ever studied that how to choose optimal weighting matrices for the parallel multisplitting two-stage iterative algorithms, we will discuss this problem in the paper.
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