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Expanding kantorovich’s theorem for solving generalized equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x) + Q(x) ϶ 0, (22.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ...
Iterative methods and their dynamics with applications: A contemporary study
(CRC Press, 2017)
Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced ...
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 ...
Directional newton methods and restricted domains
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Let F : D ⊂ ℝn → ℝ be a differentiable function. In computer graphics, we often need to compute and display the intersection C = A ⋂ B of two surfaces A and B in ℝ3 [5], [6]. If the two surfaces are explicitly given by A ...
Gauss-newton method with applications to convex optimization
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we will study the convex composite optimizations problem.
Generalized equations and newton’s and method
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In [18], G. S. Silva considered the problem of approximating the solution of the generalized equation F(x)+Q(x) ϶ 0,(11.1) where F : D → H is a Fréchet differentiable function, H is a Hilbert space with inner product ⟨., ...
Newton’s method for generalized equations using restricted domains
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter we are concerned with the study of the generalized equation F(x)+Q(x) ϶ 0, where F : D → H is a nonlinear Fréchet differentiable defined on the open subset D of the Hilbert space H, and Q : H ⇉ H is set-valued ...
Lavrentiev Regularization methods for Ill-posed equations
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
In this chapter, we consider the problem of approximately solving the nonlinear ill-posed operator equation of the form F(x) = y, (9.1) where F : D(F) ⊂ X → X is a monotone operator and X is a real Hilbert space. We denote ...
King-Werner-type methods of order 1 + √2
(Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
Iterative methods are used to generate a sequence of approximating a solution x of the nonlinear equation F(x) = 0, (10.1) where F is Fréchet-differentiable operator defined on a convex subset D of a Banach space X with ...