TY  - INPR
A1  - Michel, Volker
T1  - Fast Approximation on the 2-Sphere by Optimally Localized Approximate Identities
N2  - We introduce a method to construct approximate identities on the 2-sphere which have an optimal localization. This approach can be used to accelerate the calculations of approximations on the 2-sphere essentially with a comparably small increase of the error. The localization measure in the optimization problem includes a weight function which can be chosen under some constraints. For each choice of weight function existence and uniqueness of the optimal kernel are proved as well as the generation of an approximate identity in the bandlimited case. Moreover, the optimally localizing approximate identity for a certain weight function is calculated and numerically tested.
T3  - Schriften zur Funktionalanalysis und Geomathematik - 29 
KW  - Approximation
KW  - Polynomapproximation
KW  - L2-Approximation
KW  - Multivariate Approximation
KW  - Lokalisation
KW  - Sphäre
KW  - Numerische Mathematik
KW  - Faltung
KW  - Approximative Identität
KW  - schnelle Approximation
KW  - Konvergenz
KW  - approximate identity
KW  - fast approximation
KW  - convergence
Y1  - 2006
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1822
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-14710
ER  -