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Titel
Completeness of hierarchical spline spaces and low rank interpolation / submitted by Dominik Mokriš
VerfasserMokriš, Dominik
Begutachter / BegutachterinJuettler, Bert ; Hormann, Kai
ErschienenLinz, March 2017
Umfang106 Seiten : Illustrationen
HochschulschriftUniversität Linz, Dissertation, 2017
Anmerkung
Zusammenfassung in deutscher Sprache
SpracheEnglisch
Bibl. ReferenzOeBB
DokumenttypDissertation
Schlagwörter (DE)algebraische Vollständigkeit / hierarchische Splines / niedrig Rank Approximation / transfinite Interpolation
Schlagwörter (EN)algebraic completeness / hierarchical splines / low rank approximation / transfinite interpolation
Schlagwörter (GND)Spline / Rang <Mathematik> / Vollständigkeit / Interpolation
URNurn:nbn:at:at-ubl:1-15275 Persistent Identifier (URN)
Zugriffsbeschränkung
 Das Werk ist gemäß den "Hinweisen für BenützerInnen" verfügbar
Dateien
Completeness of hierarchical spline spaces and low rank interpolation [10.3 mb]
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Zusammenfassung (Englisch)

The thesis covers two topics. First, the completeness question is adressed, i.e., whether the hierarchical spline basis generates the entire space of piecewise polynomials on the corresponding hierarchical mesh. We identify sufficient conditions for a positive answer. We construct the truncated decoupled splines, which allow to further relax the assumptions on the mesh. Second, we discuss low-rank interpolation. A simple algorithm to generate a spline surface of rank at most 2d interpolating four boundary spline curves in R^d is presented and analyzed. Furthermore, for d = 2 a modification through a standardisation procedure is proposed in order to restore affine invariance of the algorithm. The algorithm is generalized for d = 1 to interpolate n cross-sections (not necessarily splines) in each direction with a surface of rank not exceeding n and its convergence rate is then shown to be equal to 2n.