Root finding by high order iterative methods based on quadratures

Mário M. Graça and Pedro M. Lima

Applied Mathematics and Computation, 2015, vol. 264, issue C, 466-482

Abstract: We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton–Cotes closed quadrature rules. We prove that when a quadrature rule with n + 1 nodes is used the resulting iterative method has convergence order at least n + 2, starting with the case n = 0 (which corresponds to the Newton’s method).

Keywords: Quadrature rules; Iterative methods; Newton’s method; Convergence order (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:466-482

DOI: 10.1016/j.amc.2015.04.097

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