检索结果-南通市图书馆

Convergence analysis for the secant method based on new recurrence relations

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2008年第4期23卷 447-454页

作者： BI Wei-hong REN Hong-min WU Qing-biao Department of Mathematics Zhejiang University Hangzhou 310027 China College of Information and Engineering Hangzhou Radio and TV University Hangzhou 310012China

A new convergence theorem for the secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.

关键词： secant method Banach space recurrence relation semilocal convergence Lipschitz continuous divided difference

HOMOCENTRIC CONVERGENCE BALL OF THE secant method

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2007年第3期22卷 353-365页

作者： Liang Kewei Dept. of Math. Zhejiang Univ. Hangzhou 310027 China

A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper. For every convergence theorem, a convergence ball is respectively introduced, where the hypothesis conditions of the corresponding theorem can be satisfied. Since all of these convergence balls have the same center x^＊, they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.

关键词： secant method semi-local convergence theorem local convergence theorem convergence ball,homocentric ball.

The Substitution secant/Finite Difference method for Large Scale Sparse Unconstrained Optimization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2005年第4期21卷 581-596页

作者： Hong-wei Zhang Jun-xiang Li Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

This paper studies a substitution secant/finite difference （SSFD） method for solving large scale sparse unconstrained optimization problems. This method is a combination of a secant method and a finite difference method, which depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that this method has good local convergence properties. The numerical results show that this method may be competitive with some currently used algorithms.

关键词： Unconstrained optimization substitution Hessian sparsity secant method

secant-FUZZY LINEAR REGRESSION method FOR HARMONIC COMPONENTS ESTIMATION IN A POWER SYSTEM

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

计算技术与自动化 2003年第Z1期22卷 54-57页

作者： Garba Inoussa Information Technlolgy Department Central South University of China

In order to avoid unnecessary damage of electrical equipments and installations,high quality power should be delivered to the end user and strict control on frequency should be made, Therefore, it is important to estimate the power system's harmonic components with higher accuracy. This paper presents a new approach for estimating harmonic component in a power system using secant - fuzzy linear regression method. In this approach the non - sinusoidal voltage or current waveform is written as I linear function. The coefficient of this function is assumed to be fuzzy number with a membership function that has center and spread value. The time dependent quantity is written as Taylor series with two different time dependent quantities. The objective is to use the sample obtained from the transmission line to find the power system harmonic components and frequencies. We used an experimental voltage signal from a sub power station as a numerical test.

关键词： Harmonic component Power system Fuzzy linear regression Distortion Estimation of harmonic secant method

An Easily Implementable Algorithm for Efficient Projection onto the Ordered Weighted l_(1)Norm Ball

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of the Operations Research Society of China 2023年第4期11卷 925-940页

作者： Yong-Jin Liu Jia-Jing Xu Lan-Yu Lin School of Mathematics and Statistics Fuzhou UniversityFuzhou350108FujianChina

This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine *** on Lagrangian relaxation and secant approximation method,we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of ***,we design efficient implementations for our algorithm and compare it with a semismooth Newton(SSN)algorithm and a root-finding(Root-F)*** results on a diversity of test problems show that our algorithm is superior than SSN and Root-F.

关键词： Lagrangian relaxation secant method ordered weighted l_(1)norm ball

LINEAR AND NONLINEAR DIELECTRIC PROPERTIES OF PARTICULATE COMPOSITES AT FINITE CONCENTRATION

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2006年第8期27卷 1021-1030页

作者：周萧明胡更开 Department of Applied Mechanics Beijing Institute of Technology Beijing 100081 P. R. China

An analytical method was proposed dielectric properties for particulate composites. to calculate effective linear and nonlinear The method is based on an approximate solution of two-particle interaction problem, and it can be applied to relatively high volume concentration of particles （up to 50%）. Nonlinear dielectric property was also examined by means of secant method. It is found that for low applied electric filed the proposed method is close to Stroud and Hui＇s method and for high applied electric filed it is close to Yu＇s method.

关键词： effective dielectric constants finite concentration nonlinear composite secant method

A New Modification of Newton method with Cubic Convergence

在线全文

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2021年第1期11卷 1-11页

作者： Aurelien Goudjo Louis Kouye Faculty of Science and Technic (FAST) Abomey-Calavi University (UAC) Abomey-Calavi Benin West Africa Institute of Mathematics and Physics Sciences (IMSP) Abomey-Calavi University (UAC) Porto-Novo Benin West Africa

Newton’s method is used to find the roots of a system of equations f (x) = 0. It is one of the most important procedures in numerical analysis, and its applicability extends to differential equations and integral equations. Analysis of the method shows a quadratic convergence under certain assumptions. For several years, researchers have improved the method by proposing modified Newton methods with salutary efforts. A modification of the Newton’s method was proposed by McDougall and Wotherspoon [1] with an order of convergence of 1+ √2. On a new type of methods with cubic convergence was proposed by H. H. H. Homeier [2]. In this article, we present a new modification of Newton method based on secant method. Analysis of convergence shows that the new method is cubically convergent. Our method requires an evaluation of the function and one of its derivatives.

关键词： Newton’s methods secant method Cubic Convergence Iterative method

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

基于拟牛顿方程的非线性最小二乘的新算法

高等学校计算数学学报 2010年第4期32卷 333-344页

作者：孙风建肖伟南京师范大学附属中学南京理工大学理学院

1引言我们知道,非线性最小二乘问题:minf（x）=1/2R（x）;R（x）=1/2■[r;（x）];,（1）其中x∈R;称为决策变量,R（x）=(r;（x）,r;（x）,…,r;（x）);称为在点x的残向量,目标函数f（x）的梯度和海森矩阵分别为:g（x）=▽f（x）=J（x）R... 详细信息

1引言我们知道,非线性最小二乘问题:minf（x）=1/2R（x）;R（x）=1/2■[r;（x）];,（1）其中x∈R;称为决策变量,R（x）=(r;（x）,r;（x）,…,r;（x）);称为在点x的残向量,目标函数f（x）的梯度和海森矩阵分别为:g（x）=▽f（x）=J（x）R（x）(2)▽;f（x）=C（x）+S（x）(3)其中,J（x）是R（x）在x处的Jacobian的转置.

关键词： quasi-Newton equation secant method local convergence superlinear convergence.