TY - RPRT
A1 - Frank, Karin
A1 - Heinrich, Stefan
T1 - Computing Discrepancies Related to Spaces of Smooth Periodic Functions
N2 - A notion of discrepancy is introduced, which represents the integration error on spaces of \(r\)-smooth periodic functions. It generalizes the diaphony and constitutes a periodic counterpart to the classical \(L_2\)-discrepancy as weil as \(r\)-smooth versions of it introduced recently by Paskov [Pas93]. Based on previous work [FH96], we develop an efficient algorithm for computing periodic discrepancies for quadrature formulas possessing certain tensor product structures, in particular, for Smolyak quadrature rules (also called sparse grid methods). Furthermore, fast algorithms of computing periodic discrepancies for lattice rules can easily be derived from well-known properties of lattices. On this basis we carry out numerical comparisons of discrepancies between Smolyak and lattice rules.
T3 - Interner Bericht des Fachbereich Informatik - 286
Y1 - 1996
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4928
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-49280
ER -