Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space

M. Chen, Y. Khan, Q. Wu () and A. Yildirim
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M. Chen: Zhejiang University
Y. Khan: Zhejiang University
Q. Wu: Zhejiang University
A. Yildirim: University of South Florida

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 3, No 4, 662 pages

Abstract: Abstract A Newton–Kantorovich convergence theorem of a modified Newton’s method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton–Kantorovich convergence theorems shows high accuracy of our results.

Keywords: Nonlinear equation; Modified Newton’s method; Newton–Kantorovich convergence; Gamma-condition; Fréchet differentiable; Error estimate (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-012-0237-9

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