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On HSS-based iteration methods for weakly nonlinear systems

机译：基于HSS的弱非线性系统迭代方法

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摘要

Based on separable property of the linear and the nonlinear terms and on the Hermitian and skew-Hermitian splitting of the coefficient matrix, we present the Picard-HSS and the nonlinear HSS-like iteration methods for solving a class of large scale systems of weakly nonlinear equations. The advantage of these methods over the Newton and the Newton-HSS iteration methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Hence, computational workloads and computer memory may be saved in actual implementations. Under suitable conditions, we establish local convergence theorems for both Picard-HSS and nonlinear HSS-like iteration methods. Numerical implementations show that both Picard-HSS and nonlinear HSS-like iteration methods are feasible, effective, and robust nonlinear solvers for this class of large scale systems of weakly nonlinear equations.
机译：基于线性项和非线性项的可分离性，以及系数矩阵的埃尔米特和斯维夫-希尔米特分裂，我们提出了Picard-HSS和类HSS非线性迭代方法，用于求解一类大型的弱非线性系统方程。与牛顿和牛顿-HSS迭代方法相比，这些方法的优点在于它们不需要显式构造和精确计算雅可比矩阵，而只需要求解常数系数矩阵的线性子系统。因此，在实际实现中可以节省计算工作量和计算机存储器。在合适的条件下，我们建立了Picard-HSS和非线性HSS式迭代方法的局部收敛定理。数值算例表明，对于这类弱非线性方程组的大型系统，Picard-HSS和类似非线性HSS的迭代方法都是可行，有效和鲁棒的非线性求解器。

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  • 来源
    《Applied numerical mathematics》 |2009年第12期|2923-2936|共14页
  • 作者

    Zhong-Zhi Bai; Xi Yang;

  • 作者单位

    State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China;

    State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    system of weakly nonlinear equations; HSS iteration method; inner/outer iteration scheme; nonlinear iteration scheme; local convergence;

    机译：弱非线性方程组;HSS迭代方法;内部/外部迭代方案;非线性迭代方案局部收敛;

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