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Improving order and efficiency: Composition with a modified Newton’s method

✍ Scribed by Miquel Grau-Sánchez

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
391 KB
Volume
231
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper a zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain new methods that can be generalized in Banach spaces.

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