Resumen de On generalized biparametric multipoint root finding methods with memory

Jovana Dzunic, Miodrag S. Petkovic

• 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.