http://www.cnr.it/ontology/cnr/individuo/prodotto/ID7997
Pointwise convergence of Fourier regularization for smoothing data (Articolo in rivista)
- Type
- Label
- Pointwise convergence of Fourier regularization for smoothing data (Articolo in rivista) (literal)
- Anno
- 2006-01-01T00:00:00+01:00 (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
- 10.1016/j.cam.2005.10.009 (literal)
- Alternative label
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- De Canditiis D.; De Feis I. (literal)
- Pagina inizio
- Pagina fine
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
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- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
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- Google S (literal)
- Scopu (literal)
- ISI Web of Science (WOS) (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Istituto per le Applicazioni del Calcolo 'Mauro Picone' (literal)
- Titolo
- Pointwise convergence of Fourier regularization for smoothing data (literal)
- Abstract
- The classical smoothing data problem is analyzed in a Sobolev space under the assumption of white noise. A Fourier series method based on regularization endowed with Generalized Cross Validation is considered to approximate the unknown function. This approximation is globally optimal, i.e., the Mean Integrated Squared Error reaches the optimal rate in the minimax sense. In this paper the pointwise convergence property is studied. Specifically it is proved that the smoothed solution is locally convergent but not locally optimal. Examples of functions for which the approximation is subefficient are given. It is shown that optimality and superefficiency are possible when restricting to more regular subspaces of the Sobolev space. (literal)
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