Results 11 to 20 of about 8,399 (255)
An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots
Mathematics, 2019 In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity ( m ≥ 1 ) . We use the weight function approach involving one and two parameters to
Saima Akram, Fiza Zafar, Nusrat Yasmin
doaj +3 more sources
Journal of Applied MathematicsA new family of fourth-order iterative methods for solving nonlinear equations is proposed using the weight function procedure. This family is optimal in the sense of the Kung–Traub conjecture, as it requires three function evaluations per iteration. Due
Ali Zein
doaj +2 more sources
Comparison of some optimal derivative-free three-point iterations
Journal of Numerical Analysis and Approximation Theory, 2020 We show that the well-known Khattri et al. methods and Zheng et al. methods are identical. In passing, we propose a suitable calculation formula for Khattri et al. methods.
Thugal Zhanlav, Khuder Otgondorj
doaj +7 more sources
A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency
Mathematics, 2022 A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n
Xiaofeng Wang
doaj +1 more source
An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture [PDF]
, 2022 Many multipoint iterative methods without memory for solving non-linear equations in one variable are found in the literature. In particular, there are methods that provide fourth-order, eighth-order or sixteenth-order convergence using only ...
Varona Malumbres, Juan Luis [0000-0002-2023-9946] +1 more
core +1 more source
Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques
Axioms, 2023 In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non ...
Ramandeep Behl +3 more
doaj +1 more source
Optimal eighth-order multiple root finding iterative methods using bivariate weight function
Results in Control and Optimization, 2023 In this contribution, a novel eighth-order scheme is presented for solving nonlinear equations with multiple roots. The proposed scheme comprises of three steps with the modified Newton method as its first step followed by two weighted Newton steps ...
Rajni Sharma, Ashu Bahl, Ranjita Guglani
doaj +1 more source
A new family of optimal fourth-order iterative methods for nonlinear equations
Results in Control and Optimization, 2022 A new two-parameter family of fourth-order iterative methods for the numerical solution of nonlinear equations of the form f(x)=0has been introduced and their convergence analysis have been performed.
Ahmet Yaşar Özban, Bahar Kaya
doaj +1 more source
Dynamics and Stability on a Family of Optimal Fourth-Order Iterative Methods
Algorithms, 2022 In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics.
Alicia Cordero +2 more
doaj +1 more source
Optimization by parameters in the iterative methods for solving non-linear equations
Proceedings of the Mongolian Academy of Sciences, 2021 In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence ...
Tugal Zhanlav, Khuder Otgondorj
doaj +1 more source