Local Convergence for an Improved Jarratt-type Method in Banach Space
نویسندگان
چکیده
— We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.
منابع مشابه
Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions
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.
متن کاملA Quartically Convergent Jarratt-Type Method for Nonlinear System of Equations
In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations.
متن کاملSome results about unbounded convergences in Banach lattices
Suppose E is a Banach lattice. A net in E is said to be unbounded absolute weak convergent ( uaw-convergent, for short) to provided that the net convergences to zero, weakly. In this note, we further investigate unbounded absolute weak convergence in E. We show that this convergence is stable under passing to and from ideals and sublattices. Compatible with un-convergenc, we show that ...
متن کاملAn Improved Convergence and Complexity Analysis for the Interpolatory Newton Method
We provide an improved compared to [5]–[7] local convergence analysis and complexity for the interpolatory Newton method for solving equations in a Banach space setting. The results are obtained using more precise error bounds than before [5]–[7] and the same hypotheses/computational cost. RESUMEN Nosotros entregamos aqúı un análisis de convergencia local y complejidad para el método de interpo...
متن کاملConvergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJIMAI
دوره 3 شماره
صفحات -
تاریخ انتشار 2015