Convergence Theory of Nonlinear Newton-Krylov Algorithms
Convergence Theory of Nonlinear Newton-Krylov Algorithms
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DOI：
10.1137/0804017
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发表时间：
1994-05
期刊：
影响因子：
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通讯作者：
P. Brown;Y. Saad
中科院分区：
文献类型：
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作者：
P. Brown;Y. Saad
本文给出了非线性Krylov子空间方法的一些收敛理论。这些方法的基本思想已由作者在以前的一篇文章中描述过，它们的基本思想是使用牛顿迭代的变体和Krylov子空间方法来求解雅可比线性方程组。这些方法是不精确牛顿方法的变体，其中近似牛顿方向取自小维子空间。本文的重点是将这些方法与线搜索技术、模型信赖域算法等全局策略相结合进行分析。大多数收敛结果都是为了投影到一般的子空间而不只是Krylov子空间而得到的。
This paper presents some convergence theory for nonlinear Krylov subspace methods. The basic idea of these methods, which have been described by the authors in an earlier paper, is to use variants of Newton’s iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimension. The main focus of this paper is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.