Results 11 to 20 of about 249 (128)

On the Kantorovich–Rubinstein theorem

Expositiones Mathematicae, 2011
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Kantorovich's Theorem on Newton's Method in Riemannian Manifolds

Journal of Complexity, 2002
This paper is concerned with the problem of finding a singularity of a vector field in a Riemannian manifold. The authors present an extension of Kantorovich's theorem on Newton's method for this problem in finite dimensional Riemannian manifolds.
Ferreira, O.P., Svaiter, B.F.
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Supershift properties for nonanalytic signals. [PDF]

Nanophotonics
Abstract The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this perspective, this is a notion that
Colombo F, Sabadini I, Struppa DC, Yger A.   +3 more
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]

Quant Biol
Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
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Extensions of Kantorovich-type theorems for Newton’s method [PDF]

Applicationes Mathematicae, 2020
Summary: We extend the applicability of Newton's method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.
Argyros, Ioannis K., George, Santhosh, Sahu, Daya Ram   +2 more
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Approximation Theorems for Generalized Complex Kantorovich‐Type Operators [PDF]

Journal of Applied Mathematics, 2012
The order of simultaneous approximation and Voronovskaja‐type results with quantitative estimate for complex q‐Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ ℂ : |z| < R}, R > q, the rate of approximation by the q‐Kantorovich ...
Mahmudov, N. I., Kara, M.
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Extended Newton–Kantorovich Theorem for Solving Nonlinear Equations

Foundations, 2022
The Newton–Kantorovich theorem for solving Banach space-valued equations is a very important tool in nonlinear functional analysis. Several versions of this theorem have been given by Adley, Argyros, Ciarlet, Ezquerro, Kantorovich, Potra, Proinov, Wang, et al. This result, e.g., establishes the existence and uniqueness of the solution.
Samundra Regmi, Ioannis K. Argyros, Santhosh George, Christopher I. Argyros   +3 more
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Remarks on the Afriat's Theorem and the Monge-Kantorovich Problem [PDF]

SSRN Electronic Journal, 2013
The famous Afriat's theorem from the theory of revealed preferences establishes necessary and suffient conditions for existence of utility function for a given set of choices and prices. The result on existence of a {\it homogeneous} utility function can be considered as a particular fact of the Monge-Kantorovich mass transportation theory.
Kolesnikov, Alexander V., Kudryavtseva, Olga V., Nagapetyan, Tigran   +2 more
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The Krawczyk operator and Kantorovich's theorem

Journal of Mathematical Analysis and Applications, 1990
The paper deals with the comparison of Kantorovich's test for the existence of a solution of a system of nonlinear equations of the form \(F(x)=0\) and a modification of Moore's existence test based on the Krawczyk operator. The modification involves a suitable slope instead of the Jacobian matrix \(F'\) and is proved to require less computational work
Neumaier, Arnold, Zuhe, Shen
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Kantorovich's Theorem on Newton's Method

, 2012
In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.
Ferreira, O. P., Svaiter, B. F.
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