On Newton-like methods of “bounded deterioration” using recurrent functions

Argyros, Ioannis K.; Hilout, Saïd

doi:10.1007/s00010-010-0006-5

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Remark 351

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2010

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“…and the error estimates are tighter [4][5][6][7][8][9][10][11][12]. Numerical examples for this case have been already given in [5,8,11].…”

Section: Remark 35mentioning

confidence: 97%

On the convergence of inexact two-step Newton-like algorithms using recurrent functions

Argyros

Hilout

2010

J. Appl. Math. Comput.

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Using our new concept of recurrent functions, we approximate a locally unique solution of a nonlinear equation by an inexact two-step Newton-like algorithm in a Banach space setting. Our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of a nonlinear Chandrasekhar-type integral equation appearing in radiative transfer, and a two point boundary value problem with a Green kernel are also provided in this study.

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“…and the error estimates are tighter [4][5][6][7][8][9][10][11][12]. Numerical examples for this case have been already given in [5,8,11].…”

Section: Remark 35mentioning

confidence: 97%