Polynomial degree reduction in the discrete L2-norm equals best Euclidean approximation of h-Bézier coefficients

Handle URI:
http://hdl.handle.net/10754/566149
Title:
Polynomial degree reduction in the discrete L2-norm equals best Euclidean approximation of h-Bézier coefficients
Authors:
Ait-Haddou, Rachid
Abstract:
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Springer Science + Business Media
Journal:
BIT Numerical Mathematics
Issue Date:
4-Jun-2015
DOI:
10.1007/s10543-015-0558-9
Type:
Article
ISSN:
00063835
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorAit-Haddou, Rachiden
dc.date.accessioned2015-08-12T09:30:08Zen
dc.date.available2015-08-12T09:30:08Zen
dc.date.issued2015-06-04en
dc.identifier.issn00063835en
dc.identifier.doi10.1007/s10543-015-0558-9en
dc.identifier.urihttp://hdl.handle.net/10754/566149en
dc.description.abstractWe show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrechten
dc.publisherSpringer Science + Business Mediaen
dc.subjectDegree reductionen
dc.subjectDiscrete least squaresen
dc.subjectDiscrete orthogonal polynomialsen
dc.subjecth-Bézier curvesen
dc.titlePolynomial degree reduction in the discrete L2-norm equals best Euclidean approximation of h-Bézier coefficientsen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalBIT Numerical Mathematicsen
kaust.authorAit-Haddou, Rachiden
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