论文标题
关于在较小条件下的错误条件下，牛顿法的可行性和收敛性
On the feasibility and convergence of the inexact Newton method under minor conditions on the error terms
论文作者
论文摘要
在本文中，我们介绍了一个半本地定理，以了解newton方法的可行性和收敛性，涉及序列$ x_ {k + 1} = x_k-df（x_k）^{ - 1} f（x_k）f（x_k） + r_k $，其中$ r_k $表示每个步骤中的错误。与文献中这种类型的先前结果不同，我们证明了牛顿方法的可行性是在较小的假设下，即误差$ r_k $由要计算的小常数限制，并且我们证明了有关该假设下解决方案的序列$ x_k $收敛的结果。此外，我们展示了如何应用这种方法来计算Neumann类型的两点边界值问题严格的零。最后，我们将其应用于Cahn-Hilliard方程式的版本。
In this paper we introduce a semi-local theorem for the feasibility and convergence of the inexact Newton method, regarding the sequence $x_{k+1} = x_k - Df(x_k)^{-1}f(x_k) + r_k$, where $r_k$ represents the error in each step. Unlike the previous results of this type in the literature, we prove the feasibility of the inexact Newton method under the minor hypothesis that the error $r_k$ is bounded by a small constant to be computed, and moreover we prove results concerning the convergence of the sequence $x_k$ to the solution under this hypothesis. Moreover, we show how to apply this this method to compute rigorously zeros for two-point boundary value problems of Neumann type. Finally, we apply it to a version of the Cahn-Hilliard equation.
