CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2008, v.15 no.1, pp.47-55

Argyros, Ioannis K. (Department of Mathematical Sciences, Cameron University)

Argyros, Ioannis K.. (2008). CONCERNING THE RADII OF CONVERGENCE FOR A CERTAIN CLASS OF NEWTON-LIKE METHODS. 한국수학교육학회지시리즈B:순수및응용수학, 15(1), 47-55.

복사

Abstract

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

keywords: Newton-like method, modified Newton-like method, Banach space, local convergence, radius of convergence, convergence domain

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Vol.15 No.1

CONCERNING THE RADII OF CONVERGENCE FOR A CERTAIN CLASS OF NEWTON-LIKE METHODS

CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODS

Abstract

한국수학교육학회지시리즈B:순수및응용수학