On generalized multipoint root-solvers with memory

Authors:
Jovana Dunić;Miodrag S. Petković
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 2
Cited 3

Optimal Order of One-Point and Multipoint Iteration

Journal of the ACM (JACM)
Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”

SIAM Journal on Numerical Analysis

On efficient two-parameter methods for solving nonlinear equations

Numerical Algorithms
On generalized biparametric multipoint root finding methods with memory

Journal of Computational and Applied Mathematics
A new family of Newton-type iterative methods with and without memory for solving nonlinear equations

Calcolo: a quarterly on numerical analysis and theory of computation

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Abstract

The improved versions of the Kung-Traub family and the Zheng-Li-Huang family of n-point derivative free methods for solving nonlinear equations are proposed. The convergence speed of the modified families is considerably accelerated by employing a self-correcting parameter. This parameter is calculated in each iteration using information from the current and previous iteration so that the proposed families can be regarded as the families with memory. The increase of convergence order is attained without any additional function evaluations meaning that these families with memory possess high computational efficiency. Numerical examples are included to confirm theoretical results and demonstrate convergence behaviour of the proposed methods.