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Quadrature Based Optimal Iterative Methods with Applications in High-Precision Computing

Published online by Cambridge University Press:  28 May 2015

Sanjay Kumar Khattri
Sanjay Kumar Khattri*
Affiliation:
Stord/Haugesund University College, Department of Engineering, Haugesund, Norway
*
*Corresponding author.Email address:[email protected]
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Abstract

We present a simple yet effective and applicable scheme, based on quadrature, for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on n + 1 evaluations could achieve a maximum convergence order of 2n. Through quadrature, we develop optimal iterative methods of orders four and eight. The scheme can further be applied to develop iterative methods of even higher orders. Computational results demonstrate that the developed methods are efficient as compared with many well known methods.

Keywords

65H0565D9941A25Iterative methodsfourth ordereighth orderquadratureNewtonconvergencenonlinearoptimal
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 4 , November 2012 , pp. 592 - 601
Copyright
Copyright © Global Science Press Limited 2012

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