Polynomial approximation on the sphere using scattered data (Articolo in rivista)

Type
Label
  • Polynomial approximation on the sphere using scattered data (Articolo in rivista) (literal)
Anno
  • 2008-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1002/mana.200710633 (literal)
Alternative label
  • Filbir F.; Themistoclakis W. (2008)
    Polynomial approximation on the sphere using scattered data
    in Mathematische Nachrichten
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Filbir F.; Themistoclakis W. (literal)
Pagina inizio
  • 650 (literal)
Pagina fine
  • 668 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 281 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 5 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Google S (literal)
  • Mathematical Reviews on the web (MathSciNet (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Institute for Biomathematics and Biometry, Helmholtz Center Munich, 85764 Neuherberg, Germany. CNR Istituto per la Applicazioni del Calcolo \"Mauro Picone\", sede di Napoli (literal)
Titolo
  • Polynomial approximation on the sphere using scattered data (literal)
Abstract
  • The paper tackles the problem of approximately reconstructing a real function defined on the surface of the unit sphere in the Euclidean q-dimensional space, with q>1, starting from function's samples at scattered sites. Two new operators are introduced for continuous and discrete approximation at scattered sites. Moreover precise error estimates as well as Marcinkiewicz-Zygmund inequalities are derived in every Lp space, giving concrete bounds for all the involved constants. (literal)
  • We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space R^{q+1} by using samples of f at scattered sites. A central role is played by the construction of a new operator for polynomial approximation, which is a uniformly bounded quasi-projection in the de la Vallée Poussin style, i.e. it reproduces spherical polynomials up to a certain degree and has uniformly bounded Lp operator norm for 1<=p<=infinity. Using certain positive quadrature rules for scattered sites due to Mhaskar, Narcowich and Ward, we discretize this operator obtaining a polynomial approximation of the target function which can be computed from scattered data and provides the same approximation degree of the best polynomial approximation. To establish the error estimates we use Marcinkiewicz-Zygmund inequalities, which we derive from our continuous approximating operator. We give concrete bounds for all constants in the Marcinkiewicz-Zygmund inequalities as well as in the error estimates. (literal)
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