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Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problems
(Applied Mathematics and Computation, 2014-08)
We present a local convergence analysis of the proximal Gauss-Newton method for solving penalized nonlinear least squares problems in a Hilbert space setting. Using more precise majorant conditions than in earlier studies ...
Local Convergence of the Gauss-Newton Method for Infective-Overdetermined Systems
(Journal of the Korean Mathematical Society, 2014-09)
We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information ...
Extending the convergence domain of the Secant and Moser method in Banach Space
(Journal of Computational and Applied Mathematics, 2015-12)
We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient ...
Optimizing the applicability of a theorem by F. Potra for Newton-like methods
(Applied Mathematics and Computation, 2014-09)
We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
(Numerical Algorithms, 2016-01)
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...
Expanding the applicability of the gauss-newton method for convex optimization under restricted convergence domains and majorant conditions
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
n this chapter we are concerned with the convex composite optimizations problem. This work is mainly motivated by the work in [17,23].We present a convergence analysis of Gauss-Newton method (defined by Algorithm (GNA) in ...
Ball convergence for eighth order method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a ...
Inexact gauss-newton method for least square problems
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are interested in locating a solution x of the nonlinear least squares problem: minG(x) := 1/2 F(x)TF(x), (8.1) where F is Fréchet-differentiable defined on ℝn with values in ℝm, m ≥ n.
Generalized newton method with applications
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are interested in the approximately solving the generalized equation: Find x ∈ H such that 0 ∈ F(x) + T(x). (16.1) where F : H → H is a Fr→chet differentiable function, H is a Hilbert space and T : H ⇉ ...
Iterative algorithms II
(Nova Science Publishers, 2016-01)
The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with ...