On the convergence of a Newton-like method in ℝ n and the use of Berinde's exit criterion

Rabindranath Sen, Sulekha Mukherjee and Rajesh Patra

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

Berinde has shown that Newton's method for a scalar equation f ( x ) = 0 converges under some conditions involving only f and f ′ andnot f ″ when a generalized stopping inequality is valid. LaterSen et al. have extended Berinde's theorem to the case where thecondition that f ′ ( x ) ≠ 0 need not necessarily be true. In thispaper we have extended Berinde's theorem to the class of n -dimensional equations, F ( x ) = 0 , where F : ℝ n → ℝ n , ℝ n denotes the n -dimensional Euclidean space. We have also assumedthat F ′ ( x ) has an inverse not necessarily at every point in thedomain of definition of F .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:036482

DOI: 10.1155/IJMMS/2006/36482

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