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A generalization of Müller’s iteration method based on standard information

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Abstract

For finding a root of a function f, Müler’s method is a root-finding algorithm using three values of f in every step. The natural values available are values of f and values of its first number of derivatives, called standard information. Based on standard information, we construct an iteration method with maximal order of convergence. It is a natural generalization of Müller’s iteration method.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Xinghua Wang & Peipei Tang

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  1. Xinghua Wang
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  2. Peipei Tang
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Correspondence to Peipei Tang.

Additional information

This work was partially supported by National Natural Science Foundation of China (Grant No. 10471128), NSFC (Grant No. 10731060).

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Wang, X., Tang, P. A generalization of Müller’s iteration method based on standard information. Numer Algor 48, 347–359 (2008). https://doi.org/10.1007/s11075-008-9204-9

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  • DOI: https://doi.org/10.1007/s11075-008-9204-9

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