We discuss the question of which features and/or properties make a method for solving a given problem belong to the "Newtonian class." Is it the strategy of linearization (or perhaps, second-order approximation) of the problem data (maybe only part of the problem data)? Or is it fast ...
Theorem 4. Suppose are the iterates generated by an exact proximal Newton-type method that converges to an optimal solution . The inexact proximal Newton-type method achieves the same convergence rate if . Proof. We can split into two terms: If , then convergence rate of the exact method ...
This paper proposes a Newton type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable s... R Khouja,B Mourrain,JC Yakoubsohn 被引量: 0发表: 2021年...
a newton-type iterative method -回复 题:一种新的牛顿迭代法 引言: 数值计算方法是现代科学和工程学科中的重要内容之一。其中牛顿迭代法是解非线性方程和优化问题中的一种重要数值计算方法。本文介绍一种新的牛顿迭代法,并分析其特点和应用。 一、牛顿迭代法的基本原理 牛顿迭代法是一种利用线性近似不断逼近非...
Newton-type methodSemilocal convergenceConvergence ballBanach spaces65H10The paper is concerned with the convergence problem of third-order Newton-type methods for finding zeros of nonlinear operationsin Banach spaces. Under the hypothesis that the derivative of f satisfies the weak Lipschitz condition ...
In a subsequent work, Amrein and Wihler [2] analized the percentage of convergentiterations and the average convergence order for this modif i ed Newton’s method in a nonlinear algebraic system with six roots (inarXiv:2006.00318v1 [math.NA] 30 May 2020 ...
1) Newton type method Newton型方法2) Newton-Raphson method Newton-Raphson方法 1. The presented nonlinear equations were analyzed by Newton-Raphson method. 为了准确地计算悬索桥主缆的成桥线形和无应力索长,采用悬链线单元建立了确定悬索桥主缆线形和无应力索长的计算公式;对计算悬索桥主缆线形的非...
We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pl...
Newton's methodmultilevel algorithmsmultigrid methodsunconstrained optimizationALGORITHMInspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the...
On the DSM Newton-type method 来自 Semantic Scholar 喜欢 0 阅读量: 18 作者: AG Ramm 摘要: A wide class of the operator equations F(u)=h in a Hilbert space is studied. Convergence of a Dynamical Systems Method (DSM), based on the continuous analog of the Newton method, is proved ...