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Periodic Spline Interpolation on Uniform Meshes
Author(s) -
Szyszka Uwe
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911530111
Subject(s) - mathematics , equidistant , spline (mechanical) , interpolation (computer graphics) , sobolev space , spline interpolation , polygon mesh , degree (music) , mathematical analysis , box spline , pure mathematics , geometry , bilinear interpolation , computer science , animation , statistics , physics , computer graphics (images) , structural engineering , acoustics , engineering
We examine the interpolation with periodic polynomial splines of degree d and defect r ( d ≦ r ) on equidistant partitions of the real axis and generalize known results for r = 0. We prove necessary and sufficient conditions for the existence and a certain L 2 ‐stability of the interpolants as well as their approximation properties in the scale of the periodic SOBOLEV spaces.