In this paper, the semiconvergence of parallel multisplitting iterative methods and extrapolated parallelmethods for singular linear systems is discussed. Some sufficient conditions for semiconvergence are presented ...
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In this paper, the semiconvergence of parallel multisplitting iterative methods and extrapolated parallelmethods for singular linear systems is discussed. Some sufficient conditions for semiconvergence are presented whenever the multisplittings are P-regular, sub-regular or nonnegative. As special cases the semiconvergence of parallel generalized AOR, block AOR, AOR, parallel generalized SOR, block SOR, SOR, extrapolated parallel (generalized, block) AOR and extrapolated parallel (generalized, block) SOR methods are proved. (C) 2004 Elsevier Inc. All rights reserved.
In this paper we present three modified parallel multisplitting iterative methods for solving non-Hermitian positive definite systems Ax = b. The first is a direct generalization of the standard parallel multisplittin...
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In this paper we present three modified parallel multisplitting iterative methods for solving non-Hermitian positive definite systems Ax = b. The first is a direct generalization of the standard parallel multisplitting iterative method for solving this class of systems. The other two are the iterativemethods obtained by optimizing the weighting matrices based on the sparsity of the coefficient matrix A. In our multisplitting there is only one that is required to be convergent (in a standard method all the splittings must be convergent), which not only decreases the difficulty of constructing the multisplitting of the coefficient matrix A, but also releases the constraints to the weighting matrices (unlike the standard methods, they are not necessarily be known or given in advance). We then prove the convergence and derive the convergent rates of the algorithms by making use of the standard quadratic optimization technique. Finally, our numerical computations indicate that the methods derived are feasible and efficient.
This paper givers an estimated formula of convergence rate for parallelmultisplittingiterative *** the formula,we can simplify and unify the proof of convergence of PMI_method.
This paper givers an estimated formula of convergence rate for parallelmultisplittingiterative *** the formula,we can simplify and unify the proof of convergence of PMI_method.
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