GLOBALLY CONVERGENT INEXACT NEWTON METHODS
GLOBALLY CONVERGENT INEXACT NEWTON METHODS
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DOI：
10.1137/0804022
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发表时间：
1994-05-01
影响因子：
3.1
通讯作者：
WALKER, HF
中科院分区：
文献类型：
--
作者：
EISENSTAT, SC;WALKER, HF
用于寻找F的零点的不精确牛顿方法：R（n）-> R（n）是牛顿方法的变体，其中每一步仅近似地满足线性牛顿方程，但仍降低F的局部线性模型的范数。在这里，不精确的牛顿方法制定的功能，旨在提高从任意起点的收敛。对于每一种方法，都建立了一个基本的全局收敛性结果，即在合理的假设下，如果迭代序列有一个极限点，在该极限点F'是可逆的，那么该极限点是一个解，并且该序列收敛于该极限点。在适当的情况下，证明了在解附近采用初始不精确牛顿步，因此最终可以使收敛尽可能快，直到牛顿方法的速率，通过迫使初始线性残差适当地小。主要目标是介绍和分析新的不精确牛顿方法，但也考虑到（精确）牛顿方法的“全球化”，这自然可以被视为不精确牛顿方法。
Inexact Newton methods for finding a zero of F : R(n) --> R(n) are variations of Newton's method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features designed to improve convergence from arbitrary starting points. For each method, a basic global convergence result is established to the effect that, under reasonable assumptions, if a sequence of iterates has a limit point at which F' is invertible, then that limit point is a solution and the sequence converges to it. When appropriate, it is shown that initial inexact Newton steps are taken near the solution, and so the convergence can ultimately be made as fast as desired, up to the rate of Newton's method, by forcing the initial linear residuals to be appropriately small. The primary goal is to introduce and analyze new inexact Newton methods, but consideration is also given to ''globalizations'' of (exact) Newton's method that can naturally be viewed as inexact Newton methods.