Lipschitz Conditions in Damek–Ricci Spaces

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.

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Fourier transforms of Lipschitz functions on the hyperbolic planeH2

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171298000544 ◽

1998 ◽

Vol 21 (2) ◽

pp. 397-401 ◽

Cited By ~ 5

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.

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The projected explicit Itô–Taylor methods for stochastic differential equations under locally Lipschitz conditions and polynomial growth conditions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.08.057 ◽

2019 ◽

Vol 348 ◽

pp. 161-180

Author(s):

Minggang Han ◽

Qiang Ma ◽

Xiaohua Ding

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Polynomial Growth ◽

Growth Conditions ◽

Locally Lipschitz ◽

Taylor Methods ◽

Lipschitz Conditions

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

Revista TECNIA ◽

10.21754/tecnia.v23i1.69 ◽

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.

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