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Newton's method for solving optimal shape design problems
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some results related to Newton's method in order to extend the solvability of optimal shape design problems. Moreover, some numerical examples are also presented in the chapter.
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 ...
Gauss-Newton method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present the local convergence analysis of Gauss–Newton method using the idea of restricted convergence domains, which allows us to improve previous results. Finally, some special cases and a numerical ...
Müller’s method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with approximating a solution of the equation f(x) = 0, (15.1) where f is defined on an open domain or closed domain D on a real space ℝ.
Convergence and Dynamics of a Higher-Order Method
(Symmetry, 2020-03)
Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves ...
A complex dynamical approach of Chebyshev’s method
(SeMA Journal, 2015-11)
The aim of this paper is to investigate the iterative root-finding Chebyshev’s method from a dynamical perspective. We analyze the behavior of the method applied to low degree polynomials. In this work we focus on the ...
Gauss-Newton method for convex optimization
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
The goal in this chapter is to present a finer convergence analysis of Gauss–Newton method than in earlier works in order to expand the solvability of convex composite optimizations problems. The convergence of Gauss–Newton ...