ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES

• 발행기관: 충청수학회
• 저자명: Ioannis K. Argyros Santhosh George
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 28, No. 4, 513~523쪽, 전체 11쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2015.11.30

국문 초록

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fr´echet-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third Frechet derivative. Numerical examples are also provided in this study.

목차

1. Introduction

2. Local convergence analysis

키워드

Newton-like methods R-order of convergence Banach space local convergence Frechet-derivative.