바로가기메뉴

본문 바로가기 주메뉴 바로가기
 
 

logo

  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

논문 상세

이전 다음
논문 투고

Vol.16 No.1

PDF Citation Share

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HOLDERIAN INVERSES OF OPERATORS

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2009, v.16 no.1, pp.13-18
Argyros, Ioannis K. (Cameron University, Department of Mathematics Sciences)
Argyros, Ioannis K.. (2009). ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HOLDERIAN INVERSES OF OPERATORS, 16(1), 13-18.

Abstract

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

keywords
Newton's method, Banach space, locally <tex> $H{\ddot{o}}lderian$</tex> inverses of operators, point-based approximation, semilocal convergence, successive substitutions, fixed point

참고문헌

1.

2.

(1994). . Set-Valued Analysis, 2, 291-305.

3.

(2003). . J. Comput. Appl. Math., 157(1), 169-185.

4.

5.

(1991). . Mathematics of Operations Research, 16(2), 292-309.

6.

(2008). . J. Korea Soc. Math. Edu. Ser. B: Pure Appl. Math., 15(2), 111-120.

한국수학교육학회지시리즈B:순수및응용수학

논문 투고 OA 정책