Article
A composite third order Newton–Steffensen method for solving nonlinear equations
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148 106 District Sangrur, India
Applied Mathematics and Computation (Impact Factor: 1.35). 01/2005; DOI: 10.1016/j.amc.2004.10.040 Source: DBLP

Article: On an Aitken–Newton type method
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ABSTRACT: We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes controlled by the Newton method. We obtain a local convergence result which shows that the qconvergence order of this method is 6 and its efficiency index is $\sqrt[5]{6},$ which is higher than the efficiency index of the Aitken or Newton methods. Monotone sequences are obtained for initial approximations farther from the solution, if they satisfy the Fourier condition and the nonlinear mapping satisfies monotony and convexity assumptions on the domain.Numerical Algorithms 02/2013; 62(2). · 1.13 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable conditions on the monotony and convexity of the nonlinear function, the iterations offer bilateral approximations for the solution, which can be efficiently used as a posteriori estimations.Applied Mathematics and Computation 02/2011; 217(12):5838–5846. · 1.35 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A special class of neural dynamics called Zhang dynamics (ZD), which is different from gradient dynamics (GD), has recently been proposed, generalized, and investigated for solving timevarying problems by following Zhang et al.’s design method. In view of potential digital hardware implemetation, discretetime ZD (DTZD) models are proposed and investigated in this paper for solving nonlinear timevarying equations in the form of $f(x,t)=0$ . For comparative purposes, the discretetime GD (DTGD) model and Newton iteration (NI) are also presented for solving such nonlinear timevarying equations. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear timevarying equations, as compared with the DTGD model and NI.Numerical Algorithms 12/2013; · 1.13 Impact Factor
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