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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.15 No.1

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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.
Argyros,, I. K. (2008). CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(1), 47-55.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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