FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2804736923> ?p ?o ?g. }

• W2804736923 abstract "In approximation theory, radially symmetric, (conditionally) positive definite functions, or radial basis functions (RBFs), are used to solve scattered data interpolation problems in euclidean space. The setting for a variational approach to such interpolation problems, the so-called native spaces, was constructed by several authors upon seminal work of Micchelli and of Madych and Nelson in the late 1980's. A decade later, building upon previous work by Duchon, Light and Wayne ideated an alternative approach in which the distributional theories of the Fourier transformation and the Fourier convolution play a prominent role.However, a multivariate radial function can be identified with a function on the nonnegative real axis, and its Fourier transform (which is, in turn, radial) coincides with a Hankel transform. Moreover, the natural convolution structure in the nonnegative real axis is given by (a suitable variant of) the convolution associated to the Hankel transformation, for which a distributional theory is available as well. This convolution is constructed upon a generalized translation operator, which (under minor variants) is known as Bessel, Delsarte or Hankel translation. The present thesis exploits these ideas to establish the validity of new RBF interpolation and approximation schemes where the Hankel/Delsarte translation replaces the usual one. It consists of three main chapters. In Chapter 1 we develop Light and Wayne approach to RBF interpolation, with the Hankel transformation and the Hankel convolution successfully replacing the Fourier ones. In this context, an estimate for the pointwise error of the interpolants is obtained. The study of Hankel conditionally positive definiteness (connecting our interpolation spaces with the standard native spaces) is initiated, and some examples of basis functions are given. Numerical experiments are appended.The new interpolation spaces are endowed with a seminorm which involves a weight and is expressed in terms of the Hankel transform of each function (indirect seminorm). In Chapter 2 we discuss essentially two special classes of weights (so-called of type I and type II) that allow to write these indirect seminorms in direct form, that is, in terms of the function itself rather than its Hankel transform, thus leading to more convenient error estimates. Fairly general conditions, which are shown to be satisfied by type II weights, are formulated in order to guarantee the density in the interpolation spaces of some other spaces arising naturally in the theory. Finally, we obtain explicit representations of the basis functions, the members of the interpolation spaces and their higher-order Bessel derivatives, along with some polynomial bounds for them.A particularly interesting outcome of standard RBF interpolation concerns approximation by RBF neural networks (RBFNNs), which constitute a central theme in neurocomputing as well as in many other areas as diverse as finance, medicine, biology, geology, engineering and physics. In Chapter 3 we prove that the family of RBFNNs which results from replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, is dense (in neurocomputing terminology: has the universal approximation property) in spaces of weighted p-integrable functions and in spaces of continuous functions, endowed with certain natural topologies. Furthermore, a characterization of those kernels yielding universal approximation is obtained for p=1 and p=2, provided that the smoothing factor is allowed to vary across the kernel nodes. We end by solving the closely related question of obtaining analogues of the celebrated Wiener and Wiener-Pitt tauberian theorems for the Delsarte translation and the Fourier-Bessel transformation." @default.
• W2804736923 created "2018-06-01" @default.
• W2804736923 creator A5027508368 @default.
• W2804736923 date "2014-01-01" @default.
• W2804736923 modified "2023-09-27" @default.
• W2804736923 title "Interpolation and approximation by delsarte translates of radial basis functions" @default.
• W2804736923 hasPublicationYear "2014" @default.
• W2804736923 type Work @default.
• W2804736923 sameAs 2804736923 @default.
• W2804736923 citedByCount "0" @default.
• W2804736923 crossrefType "journal-article" @default.
• W2804736923 hasAuthorship W2804736923A5027508368 @default.
• W2804736923 hasConcept C102519508 @default.
• W2804736923 hasConcept C104114177 @default.
• W2804736923 hasConcept C107706756 @default.
• W2804736923 hasConcept C134306372 @default.
• W2804736923 hasConcept C137800194 @default.
• W2804736923 hasConcept C154945302 @default.
• W2804736923 hasConcept C33923547 @default.
• W2804736923 hasConcept C41008148 @default.
• W2804736923 hasConcept C45347329 @default.
• W2804736923 hasConcept C50644808 @default.
• W2804736923 hasConcept C57640460 @default.
• W2804736923 hasConcept C98856871 @default.
• W2804736923 hasConceptScore W2804736923C102519508 @default.
• W2804736923 hasConceptScore W2804736923C104114177 @default.
• W2804736923 hasConceptScore W2804736923C107706756 @default.
• W2804736923 hasConceptScore W2804736923C134306372 @default.
• W2804736923 hasConceptScore W2804736923C137800194 @default.
• W2804736923 hasConceptScore W2804736923C154945302 @default.
• W2804736923 hasConceptScore W2804736923C33923547 @default.
• W2804736923 hasConceptScore W2804736923C41008148 @default.
• W2804736923 hasConceptScore W2804736923C45347329 @default.
• W2804736923 hasConceptScore W2804736923C50644808 @default.
• W2804736923 hasConceptScore W2804736923C57640460 @default.
• W2804736923 hasConceptScore W2804736923C98856871 @default.
• W2804736923 hasLocation W28047369231 @default.
• W2804736923 hasOpenAccess W2804736923 @default.
• W2804736923 hasPrimaryLocation W28047369231 @default.
• W2804736923 hasRelatedWork W1489242104 @default.
• W2804736923 hasRelatedWork W165475905 @default.
• W2804736923 hasRelatedWork W1976992261 @default.
• W2804736923 hasRelatedWork W2009962720 @default.
• W2804736923 hasRelatedWork W2021260467 @default.
• W2804736923 hasRelatedWork W2039356556 @default.
• W2804736923 hasRelatedWork W205987120 @default.
• W2804736923 hasRelatedWork W2098376290 @default.
• W2804736923 hasRelatedWork W2217138748 @default.
• W2804736923 hasRelatedWork W2610766251 @default.
• W2804736923 hasRelatedWork W2624802872 @default.
• W2804736923 hasRelatedWork W2625428075 @default.
• W2804736923 hasRelatedWork W2863021106 @default.
• W2804736923 hasRelatedWork W2887712198 @default.
• W2804736923 hasRelatedWork W3098144539 @default.
• W2804736923 hasRelatedWork W3159330115 @default.
• W2804736923 hasRelatedWork W42465599 @default.
• W2804736923 hasRelatedWork W606575930 @default.
• W2804736923 hasRelatedWork W626995375 @default.
• W2804736923 hasRelatedWork W69717090 @default.
• W2804736923 isParatext "false" @default.
• W2804736923 isRetracted "false" @default.
• W2804736923 magId "2804736923" @default.
• W2804736923 workType "article" @default.