scholarly journals Lipschitz Conditions in Damek–Ricci Spaces

2021 ◽  
Vol 359 (6) ◽  
pp. 675-685
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Lipschitz Conditions

scholarly journals Gauss–Newton–Secant Method for Solving Nonlinear Least Squares Problems under Generalized Lipschitz Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 158
Author(s):  
Ioannis K. Argyros ◽  
Stepan Shakhno ◽  
Roman Iakymchuk ◽  
Halyna Yarmola ◽  
Michael I. Argyros
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Local Convergence ◽  
Nonlinear Least Squares ◽  
Computational Effort ◽  
Least Squares Problems ◽  
Restricted Region ◽  
Convergence Orders ◽  
Operator Decomposition ◽  
Lipschitz Conditions

We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. We consider the case of both zero and nonzero residuals and determine their convergence orders. We use two types of Lipschitz conditions (center and restricted region conditions) to study the convergence of the method. Moreover, we obtain a larger radius of convergence and tighter error estimates than in previous works. Hence, we extend the applicability of this method under the same computational effort.

scholarly journals Fourier transforms of Lipschitz functions on the hyperbolic planeH2

1998 ◽  
Vol 21 (2) ◽  
pp. 397-401 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Hyperbolic Plane ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Order Of Magnitude ◽  
Complex Valued ◽  
Lipschitz Conditions

The purpose of the present work is to study the order of magnitude of the Fourier transformsfˆ(λ)for largeλof complex-valued functionsf(z)sating certain Lipschitz conditions in the non-Euclidean hyperbolic planeH2.

scholarly journals UNA NUEVA FORMA DEL TEOREMA DE KANTOROVICH PARA EL ME´ TODO DE NEWTON

2017 ◽  
Vol 23 (1) ◽  
pp. 79
Author(s):  
Leopoldo Paredes Soria ◽  
Pedro Canales García
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Unique Solution ◽  
Newton’S Method ◽  
Convergence Theorem ◽  
Newton's Method ◽  
Convergence Condition ◽  
Palabras Clave ◽  
Lipschitz Conditions

Una nueva forma de convergencia de tipo Kantorovich para el me´todo de Newton es establecido para aproximarse localmente a una solucio´n u´nica de la ecuacio´n F (x) = 0 definido sobre un espacio de Banach. Se asume que el operador F es dos veces diferenciable Fre´chet, y que Fr, F rr satisface las condiciones de Lipschitz. Nuestra condicio´n de convergencia difiere de los me´todos conocidos y por lo tanto tiene un valor teo´rico y pra´ctico Palabras clave.-Operador lineal, Diferenciable Fre´chet, Sucesio´n convergente, Unicidad. ABSTRACTA new Kantorovich-type convergence theorem for Newton’s method is established for approximating a locally unique solution of an equation F (x) = 0 defined on a Banach space. It is assumed that the operator F is twice Fre´chet differentiable, and that Fr, F rr satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value. Keywords.-Linear operator, Differentiable Fre´chet, Convergent succession, Uniqueness.

Inexact Newton method under weak and center-weak Lipschitz conditions

2013 ◽  
Vol 40 (2) ◽  
pp. 237-258
Author(s):  
I. K. Argyros ◽  
S. K. Khattri
Keyword(s):  
Newton Method ◽  
Inexact Newton Method ◽  
Lipschitz Conditions

Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions

2019 ◽  
Vol 40 (1) ◽  
pp. 199-210
Author(s):  
Ioannis K. Argyros ◽  
Yeol Je Cho ◽  
Santhosh George ◽  
Yibin Xiao
Keyword(s):  
Local Convergence ◽  
Lipschitz Conditions
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