Results 21 to 30 of about 1,971 (87)

A simplified proof of the Kantorovich theorem for solving equations using telescopic series

Journal of Numerical Analysis and Approximation Theory, 2015
We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting.
Ioannis K. Argyros, Hongmin Ren
doaj   +2 more sources

Generalized Newton's Method based on Graphical Derivatives [PDF]

, 2010
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have
Hoheisel, T., Kanzow, C., Mordukhovich, B. S., Phan, H.   +3 more
core   +2 more sources

Improving Newton's method performance by parametrization: the case of Richards equation [PDF]

, 2016
The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for the ...
Brenner, Konstantin, Cancès, Clément
core   +3 more sources

Rigorous Enclosures of Solutions of Neumann Boundary Value Problems

, 2020
This paper is dedicated to the problem of isolating and validating zeros of non-linear two point boundary value problems. We present a method for such purpose based on the Newton-Kantorovich Theorem to rigorously enclose isolated zeros of two point ...
Gameiro, Marcio, Nolasco, Victor, Ramos, Eduardo   +2 more
core  

Newton Method on Riemannian Manifolds: Covariant Alpha-Theory

, 2003
In this paper we study quantitative aspects of Newton method for finding zeros of mappings f: M_n -> R^n and vector fields X: M_x ...
Dedieu, Jean-Pierre, Malajovich, Gregorio, Priouret, Pierre   +2 more
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A modified Newton-secant method for solving nonsmooth generalized equations

Mathematical Modelling and Analysis
In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition.
Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza   +3 more
doaj   +1 more source

The Fréchet–Newton Scheme for SV-HJB: Stability Analysis via Fixed-Point Theory

Axioms
This paper investigates the optimal portfolio control problem under a stochastic volatility model, whose dynamics are governed by a highly nonlinear Hamilton–Jacobi–Bellman equation.
Mehran Paziresh, Karim Ivaz, Mariyan Milev   +2 more
doaj   +1 more source

On approximating the solutions of equations by the chord method and a method of Aitken-Steffensen type

Journal of Numerical Analysis and Approximation Theory, 2013
In [13] we have studied the existence and the convergence of iterative methods that use generalized abstract divided differences (this notion being defined there). We have indicated a construction model for these differences as well.
Adrian Diaconu
doaj   +2 more sources

On the solution of generalized equations and variational inequalities

Cubo, 2011
Uko and Argyros provided in [18] a Kantorovich-type theorem on the existence and uniqueness of the solution of a generalized equation of the form 𝓕 (𝓤)+ 𝓖(𝓤) ∋ 0, where f is a Fréchet-differentiable function, and g ...
Ioannis K Argyros, Saïd Hilout
doaj  

On the comparison of a weak variant of the Newton–Kantorovich and Miranda theorems

Journal of Computational and Applied Mathematics, 2004
The author [J. Comput. Appl. Math. 157, 169--185 (2003; Zbl 1030.65060)] has shown a semi-local convergence theorem under weaker assumptions than those of the Newton-Kantorovich theorem. Operators satisfying the weakened Newton-Kantorovich conditions are shown to satisfy the conditions of the weakened Miranda theorem.
openaire   +2 more sources