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http://dx.doi.org/10.11568/kjm.2019.27.4.1005

CONVERGENCE OF A CONTINUATION METHOD UNDER MAJORANT CONDITIONS  

Nisha, Shwet (Department of Mathematics Central University of Jharkhand)
Parida, P.K. (Department of Mathematics Central University of Jharkhand)
Kumari, Chandni (Department of Mathematics Central University of Jharkhand)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 1005-1025 More about this Journal
Abstract
The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.
Keywords
Continuation method; Majorant conditions; Kantorovich-type convergence criterion; Smale-type convergence criterion;
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