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Improvements of Modified Newton-Raphson Method

Improvements of Modified Newton-Raphson Method
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On Convergence Domains of Newton's and Modified Newton Methods

Numerical Functional Analysis and Optimization, 2005
We analyze convergence domains of Newton's and the modified Newton methods for solving operator equations in Banach spaces assuming first that the operator in question is ω-smooth in a ball centere...
A Galperín
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Expanding the applicability of Newton’s method and of a robust modified Newton’s method

Applicationes Mathematicae, 2021
Summary: Newton's method cannot be used to approximate a solution of a nonlinear equation when the derivative of the function is singular or almost singular. To overcome this problem a modified Newton's method may be used. The Newton-Kantorovich theorem is used to show its convergence. The convergence domain of this method is small in general.
Argyros, Ioannis K., George, Santhosh
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A Modified Newton–Raphson Method

Communications in Numerical Methods in Engineering, 2004
AbstractIn this paper, we propose the following modified Newton–Raphson iteration formulation: In case r=1, the obtained formulation reduces to the Newton–Raphson formulation. The present technique circumvent pitfalls of the Newton–Raphson iteration method. Some examples are illustrated. Copyright © 2004 John Wiley & Sons, Ltd.
Ji-Huan He
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On Modified Newton Methods With Cubic Convergence

Applied Mathematics and Computation, 2006
Modified Newton methods are discussed for solving nonlinear single real equation \(f(x)=0\). It is shown that the proposed methods have the third-order convergence. Numerical examples are given.
Jisheng Kou, Xiuhua Wang
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A Modified Newton’s Method for Unconstrained Minimization

SIAM Journal on Numerical Analysis, 1979
Newton’s method for the minimization of a function of several variables presents difficulties in the case where the Hessian matrix is not positive definite. Various modifications are known. Any such modification uses a factorization of the Hessian. This paper suggests using the symmetric decomposition established in an earlier paper by the same authors
Kaniel, Shmuel, Dax, Achiya
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A modified Newton-like method for nonlinear equations

Computational and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song Wu, Haijun Wang
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A modified Newton method for minimization

Journal of Optimization Theory and Applications, 1977
Some promising ideas for minimizing a nonlinear function, whose first and second derivatives are given, by a modified Newton method, were introduced by Fiacco and McCormick (Ref. 1). Unfortunately, in developing a method around these ideas, Fiacco and McCormick used a potentially unstable, or even impossible, matrix factorization.
Fletcher, R., Freeman, T. L.
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