Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder | Zendy

Isaac Fried | Zendy

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Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder

Author(s) -

Isaac Fried

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/108976

Subject(s) - remainder , taylor series , mathematics , simple (philosophy) , nonlinear system , asymptotic expansion , function (biology) , root (linguistics) , iterative method , order (exchange) , bracket , mathematical optimization , mathematical analysis , arithmetic , philosophy , linguistics , physics , epistemology , finance , quantum mechanics , evolutionary biology , economics , biology , mechanical engineering , engineering

The asymptotic form of the Taylor-Lagrange remainder is used to derive some new, efficient, high-order methods to iteratively locate the root, simple or multiple, of a nonlinear function. Also derived are superquadratic methods that converge contrarily and superlinear and supercubic methods that converge alternatingly, enabling us not only to approach, but also to bracket the root

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