Optimal derivative-free root finding methods based on the Hermite interpolation

Volume 9, Issue 6, pp 4427--4435 http://dx.doi.org/10.22436/jnsa.009.06.82

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Authors

Nusrat Yasmin - Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan. Fiza Zafar - Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan. Saima Akram - Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan.

Abstract

We develop n-point optimal derivative-free root finding methods of order \(2^n\), based on the Hermite interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that the optimal order of convergence of the transformed methods is preserved, according to the conjecture of Kung and Traub. To check the effectiveness and reliability of the newly presented methods, different type of nonlinear functions are taken and compared.

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Keywords

• Root finding methods
• optimal order of convergence
• derivative approximation
• Hermite interpolation.

MSC

•  65H04
•  65H05

References

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