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On modified Newton methods with cubic convergence
Applied Mathematics and Computation, 2006Modified 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.
Kou, Jisheng, Li, Yitian, Wang, Xiuhua
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TDOA location based on modified Newton method
2016 IEEE 13th International Conference on Signal Processing (ICSP), 2016In the TDOA location of multi-Radar System, steepest descent method which is the commonly method has small amount of calculation while it's jagged, slow convergence, and the step size is difficult to choose. Although the genetic algorithm could accurately solve the global optimal solution, but the speed of convergence could slow down with the iterative
Lei Yang, Jianshu Cao, Wei Yang
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On Convergence Domains of Newton's and Modified Newton Methods
Numerical Functional Analysis and Optimization, 2005We 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...
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Application of newton modified barrier method to structural optimization
Computers & Structures, 1993Summary: This paper presents the application of the Newton modified barrier method to obtain a minimum weight structure with constraints on displacements and minimum sizes. The solution to the problem is obtained via minimizing the modified barrier function (MBF) at each step by using the Newton method and updating Lagrange multipliers.
Khot, N. S. +3 more
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A Modified Quasi‐Newton Method for Optimization in Simulation
International Transactions in Operational Research, 1997Optimization in Simulation is an important problem often encountered in system behavior investigation; however, the existing methods such as response surface methodology and stochastic approximation method are inefficient. This paper presents a modification of a quasi‐Newton method, in which the parameters are determined from some numerical experiments.
Kao, Chiang +2 more
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Modified Newton method in circular interval arithmetic
Journal of Optimization Theory and Applications, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Numerical Functional Analysis and Optimization, 2008
Regularized versions of continuous analogues of Newton's method and modified Newton's method for obtaining approximate solutions to a nonlinear ill-posed operator equation of the form F(u) = f, where F is a monotone operator defined from a Hilbert space H into itself, have been studied in the literature.
M. T. Nair, P. Ravishankar
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Regularized versions of continuous analogues of Newton's method and modified Newton's method for obtaining approximate solutions to a nonlinear ill-posed operator equation of the form F(u) = f, where F is a monotone operator defined from a Hilbert space H into itself, have been studied in the literature.
M. T. Nair, P. Ravishankar
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Concerning the Convergence of a Modified Newton-Like Method
Zeitschrift für Analysis und ihre Anwendungen, 1999We provide sufficient convergence conditions for a certain Newton-like method to a locally unique solution of a nonlinear equation in a Banach space. We assume that the Fréchet-derivative of the operator involved satisfies in some sense uniformly continuous conditions, which are weaker than earlier ones.
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Modified Newton-Raphson methods for preliminary orbit determination
Celestial Mechanics, 1969Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy.
Pitkin, E. T., Carpenter, G. C.
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Parameter Selection for Modified Newton Methods for Function Minimization
SIAM Journal on Numerical Analysis, 1970The stability of Newton’s methods for function minimization, or variants of it such as quasi-Newton or Newton–Raphson methods, can be improved by modifying the acceleration matrix by adding a scalar parameter to the diagonal elements. It can be further improved by optimizing the function in the direction of the search vector.
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