scholarly journals Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Qingbiao Wu ◽  
Jueliang Hu
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Convergence Theorems ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Numerical Examples ◽  
Halley’S Method ◽  
Halley's Method

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

Semilocal Convergence Theorem for a Newton-like Method

2017 ◽  
Vol 7 (3) ◽  
pp. 482-494
Author(s):  
Rong-Fei Lin ◽  
Qing-Biao Wu ◽  
Min-Hong Chen ◽  
Lu Liu ◽  
Ping-Fei Dai
Keyword(s):  
Error Estimate ◽  
Nonlinear Equations ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Weak Condition ◽  
Third Order ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Semilocal Convergence Theorem

AbstractThe semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

scholarly journals Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

1986 ◽  
Vol 9 (3) ◽  
pp. 583-587
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

On the convergence of Halley’s method for simultaneous computation of polynomial zeros

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Petko D. Proinov ◽  
Stoil I. Ivanov
Keyword(s):  
Convergence Theorem ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
Polynomial Zeros ◽  
Convergence Theorems ◽  
Halley’S Method ◽  
Halley's Method ◽  
Semilocal Convergence Theorem

AbstractIn this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.

scholarly journals Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yueqing Zhao ◽  
Rongfei Lin ◽  
Zdenek Šmarda ◽  
Yasir Khan ◽  
Jinbiao Chen ◽  
...  
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Operator Equation ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Nonlinear Operator Equation ◽  
Jarratt Method ◽  
Semilocal Convergence Theorem

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.

scholarly journals On the Convergence Ball and Error Analysis of the Modified Secant Method

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Rongfei Lin ◽  
Qingbiao Wu ◽  
Minhong Chen ◽  
Xuemin Lei
Keyword(s):  
Error Estimate ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Secant Method ◽  
Convergence Properties ◽  
Fibonacci Series ◽  
Convergence Ball ◽  
Numerical Examples ◽  
Iteration Methods ◽  
Local Convergence Theorem

We aim to study the convergence properties of a modification of secant iteration methods. We present a new local convergence theorem for the modified secant method, where the derivative of the nonlinear operator satisfies Lipchitz condition. We introduce the convergence ball and error estimate of the modified secant method, respectively. For that, we use a technique based on Fibonacci series. At last, some numerical examples are given.

scholarly journals Newton-Kantorovich convergence theorem of a new modified Halley’s method family in a Banach space

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Rongfei Lin ◽  
Yueqing Zhao ◽  
Zdeněk Šmarda ◽  
Qingbiao Wu ◽  
Yasir Khan
Keyword(s):  
Banach Space ◽  
Convergence Theorem ◽  
Halley’S Method ◽  
Halley's Method
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