On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
复制标题
DOI：
10.1137/040611653
复制
发表时间：
2005-05
期刊：
影响因子：
--
通讯作者：
Hengbin An
中科院分区：
文献类型：
--
作者：
Hengbin An
加性施瓦茨预处理不精确牛顿法（ASPIN）是最近提出的[X.- C. Cai和D. E.\凯斯，{\it SIAM J. Sci.\} Comput.}，24（2002），pp. [183- 200]求解具有非平衡非线性项的非线性方程组。虽然ASPIN方法已经成功地用于求解一些困难的非线性方程组，但自提出以来，其收敛性还没有得到研究。本文研究了ASPIN方法的收敛性，结果表明该方法是局部收敛的。此外，还讨论了ASPIN方法的收敛速度，所得结果与不精确Newton方法的结果相似。
The additive Schwarz preconditioned inexact Newton (ASPIN) method was recently introduced [X.-C. Cai and D. E.\ Keyes, {\it SIAM J. Sci.\ Comput.}, 24 (2002), pp. 183--200] to solve the systems of nonlinear equations with nonbalanced nonlinearities. Although the ASPIN method has successfully been used to solve some difficult nonlinear equations, its convergence property has not been studied since it was proposed. In this paper, the convergence property of the ASPIN method is studied, and the obtained result shows that this method is locally convergent. Furthermore, the convergence rate for the ASPIN method is discussed and the obtained result is similar to that of the inexact Newton method.