Abstract
Starting from the recently discovered orthogonality relations for cardinal B-splines over the real line we derive suitably modified bilinear forms providing orthonormality over bounded intervals. We conjecture that these bilinear forms are positive definite and therefore inner products for B-splines of arbitrary order n ∈ IN. For n ≤ 8, this is verified by explicit computation of the corresponding matrices. Further, applications to approximation theory are discussed.
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© 1997 Springer-Verlag Berlin Heidelberg
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Reif, U. (1997). Orthogonality Relations for Cardinal B-Splines over Bounded Intervals. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_5
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DOI: https://doi.org/10.1007/978-3-642-60607-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61883-6
Online ISBN: 978-3-642-60607-6
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