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http://dx.doi.org/10.14317/jami.2015.061

HIGHER ORDER INTERVAL ITERATIVE METHODS FOR NONLINEAR EQUATIONS  

Singh, Sukhjit (Department of Mathematics, IIT Kharagpur)
Gupta, D.K. (Department of Mathematics, IIT Kharagpur)
Publication Information
Journal of applied mathematics & informatics / v.33, no.1_2, 2015 , pp. 61-76 More about this Journal
Abstract
In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.
Keywords
Newton's method; Potra's method; Convergence analysis; Efficiency; Error bounds; Optimization problems;
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