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

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  • Isaac Fried

Abstract

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.

Suggested Citation

  • Isaac Fried, 2014. "Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-14, July.
    • Handle: RePEc:hin:jnljam:108976
    DOI: 10.1155/2014/108976
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