HYBRID KRYLOV METHODS FOR NONLINEAR-SYSTEMS OF EQUATIONS
HYBRID KRYLOV METHODS FOR NONLINEAR-SYSTEMS OF EQUATIONS
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DOI：
10.1137/0911026
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发表时间：
1990-05-01
期刊：
影响因子：
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通讯作者：
SAAD, Y
中科院分区：
文献类型：
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作者：
BROWN, PN;SAAD, Y
基于Krylov子空间投影方法，讨论了求解非线性方程组的Newton类迭代格式的几种实现。最简单的这类方法是牛顿算法，其中（线性）Krylov方法用于近似求解雅可比系统。这类方法被称为牛顿-克雷洛夫算法。为了提高这些基本算法的全局收敛性，提出了基于Powell狗腿策略的混合算法，以及线性回溯算法。在本文中考虑的方法类的主要优点是，雅可比矩阵是从来没有明确需要。
Several implementations of Newton-like iteration schemes based on Krylov subspace projection methods for solving nonlinear equations are considered. The simplest such class of methods is Newton’s algorithm in which a (linear) Krylov method is used to solve the Jacobian system approximately. A method in this class is referred to as a Newton–Krylov algorithm. To improve the global convergence properties of these basic algorithms, hybrid methods based on Powell’s dogleg strategy are proposed, as well as linesearch backtracking procedures. The main advantage of the class of methods considered in this paper is that the Jacobian matrix is never needed explicitly.