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Stability results for approximation by positive definite functions on SO(3).

J. Approx. Theory 153, 170-183 (2008)
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We consider interpolation methods defined by positive definite functions on a locally compact group G. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented, and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally, we apply our results to construct well-localized positive definite basis functions having nice stability properties on the rotation group SO(3).
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter scattered data approximation; rotation group; positive definite functions; stability
ISSN (print) / ISBN 0021-9045
e-ISSN 1096-0430
Quellenangaben Band: 153, Heft: 2, Seiten: 170-183 Artikelnummer: , Supplement: ,
Verlag Elsevier
Begutachtungsstatus Peer reviewed