On generalized biparametric multipoint root finding methods with memory

• Autores: Jovana Dzunic, Miodrag S. Petkovic
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 362-375
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.05.013
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• Resumen

  • A general family of biparametric n-point methods with memory for solving nonlinear equations is proposed using an original accelerating procedure with two parameters.

    This family is based on derivative free classes of n-point methods without memory of interpolatory type and Steffensen-like method with two free parameters. The convergence rate of the presented family is considerably increased by self-accelerating parameters which are calculated in each iteration using information from the current and previous iteration and Newton�s interpolating polynomials with divided differences. The improvement of convergence order is achieved without any additional function evaluations so that the proposed family has a high computational efficiency. Numerical examples are included to confirm theoretical results and demonstrate convergence behavior of the proposed methods.