A New-Mean Type Variant of Newton´s Method for Simple and Multiple Roots

Manoj Kumar Singh; Arvind K. Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V49P524

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 49 | Number 3 | Year 2017 | Article Id. IJMTT-V49P524 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P524

A New-Mean Type Variant of Newton´s Method for Simple and Multiple Roots

Manoj Kumar Singh, Arvind K. Singh

Citation :

Manoj Kumar Singh, Arvind K. Singh, "A New-Mean Type Variant of Newton´s Method for Simple and Multiple Roots," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 3, pp. 174-177, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P524

Abstract

A new variant of Newton's method based on heronian-mean for multiple root has been developed and their convergence properties have been discussed. In addition to numerical tests verifying the theory, a comparison of the results for the proposed method and some of the existing ones have also been given. Convergence analysis shows that the efficiency index of proposed method is 1.442, which is better than Newton´s method (1.414).

Keywords

Newton's method, Iteration function, Order of convergence, Function evaluations, Efficiency index.

References

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