## Abstract

For the block system of weakly nonlinear equations Ax=G(x), where A∈R^{n×n} is a large sparse block matrix and G:R^{n}→R^{n} 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∈R^{n×n} is a block H-matrix of different types and G:R^{n}→R^{n} 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.

Original language | English |
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Pages (from-to) | 271-286 |

Number of pages | 16 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 110 |

Issue number | 2 |

DOIs | |

Publication status | Published - 30 Oct 1999 |

## Keywords

- 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