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A Newton-type method and its application [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space.
V. Antony Vijesh, P. V. Subrahmanyam
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On Fractional Newton-Type Method for Nonlinear Problems
Journal of Mathematics, 2022 The current manuscript is concerned with the development of the Newton–Raphson method, playing a significant role in mathematics and various other disciplines such as optimization, by using fractional derivatives and fractional Taylor series expansion ...
Mine Aylin Bayrak +2 more
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A Newton-type technique for solving absolute value equations
Alexandria Engineering Journal, 2023 The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under
Alamgir Khan +7 more
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A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula
International Journal of Analysis and Applications, 2023 The conjugate gradient and Quasi-Newton methods have advantages and drawbacks, as although quasi-Newton algorithm has more rapid convergence than conjugate gradient, they require more storage compared to conjugate gradient algorithms.
Mardeen Sh. Taher, Salah G. Shareef
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Newton-MR: Inexact Newton Method with minimum residual sub-problem solver
EURO Journal on Computational Optimization, 2022 We consider a variant of inexact Newton Method [20,40], called Newton-MR, in which the least-squares sub-problems are solved approximately using Minimum Residual method [79].
Fred Roosta +3 more
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Conformable fractional Newton-type inequalities with respect to differentiable convex functions
Journal of Inequalities and Applications, 2023 The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly ...
Cihan Ünal +2 more
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Extended Newton-type Method for Generalized Equations with Hölderian Assumptions
Communications in Advanced Mathematical Sciences, 2021 In the present paper, we consider the generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable on a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\mathcal X\to \mathcal Y$ is ...
Mohammed Harunor Rashid +1 more
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Alexandria Engineering Journal, 2022 Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay.
N. Senu +3 more
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Mathematics, 2020 In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives.
Giro Candelario +2 more
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Mathematics, 2023 In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives.
Giro Candelario +3 more
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