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A class of asynchronous multisplitting two-stage iterations for large sparse block systems of weakly nonlinear equations

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Publication details

JournalJournal of Computational and Applied Mathematics
DatePublished - 30 Oct 1999
Issue number2
Number of pages16
Pages (from-to)271-286
Original languageEnglish


For the block system of weakly nonlinear equations Ax=G(x), where A∈Rn×n is a large sparse block matrix and G:Rn→Rn is a block nonlinear mapping having certain smoothness properties, we present a class of asynchronous parallel multisplitting block two-stage iteration methods in this paper. These methods are actually the block variants and generalizations of the asynchronous multisplitting two-stage iteration methods studied by Bai and Huang (Journal of Computational and Applied Mathematics 93(1) (1998)13-33), and they can achieve high parallel efficiency of the multiprocessor system, especially, when there is load imbalance. Under quite general conditions that A∈Rn×n is a block H-matrix of different types and G:Rn→Rn is a block P-bounded mapping, we establish convergence theories of these asynchronous multisplitting block two-stage iteration methods. Numerical computations show that these new methods are very efficient for solving the block system of weakly nonlinear equations in the asynchronous parallel computing environment.

    Research areas

  • 65H10, 65W05, Asynchronous parallel method, Block system of weakly nonlinear equations, Convergence theory, CR: G1.3, Matrix multisplitting, Block two-stage interation, Block H-matrix

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