Approximation of the Tikhonov regularization parameter through Aitken's extrapolation

Fika, Paraskevi

doi:10.1016/j.apnum.2023.04.008

Cited by 1 publication

(1 citation statement)

References 23 publications

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“…There are a variety of numerical strategies that can be applied and were recently updated, i.e., Adomian decomposition [1], Aitken extrapolation [2], bisection [3], Chebyshev-Halley [4], Chun-Neta [5], collocation [6], Galerkin [7], homotopy perturbation [8] and Jarratt [9] methods, Nash-Moser iteration [10], Newton-Raphson [11], Osada [12] and Ostrowski [13] methods, Picard iteration [14], quadrature formulas [15,16], super-Halley [17] and Thukral [18] and Traub-Steffensen [19] methods.…”

Section: Introductionmentioning

confidence: 99%

Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications

Sharma,

Panday,

Mittal

et al. 2023

Mathematics

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In this paper, we propose a new fifth-order family of derivative-free iterative methods for solving nonlinear equations. Numerous iterative schemes found in the existing literature either exhibit divergence or fail to work when the function derivative is zero. However, the proposed family of methods successfully works even in such scenarios. We extended this idea to memory-based iterative methods by utilizing self-accelerating parameters derived from the current and previous approximations. As a result, we increased the convergence order from five to ten without requiring additional function evaluations. Analytical proofs of the proposed family of derivative-free methods, both with and without memory, are provided. Furthermore, numerical experimentation on diverse problems reveals the effectiveness and good performance of the proposed methods when compared with well-known existing methods.

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