On the Dimension of the Spline Space S 2 1 (Δ) in Special Cases

Meyling, R. H. J. Gmelig; Pfluger, P. R.

doi:10.1007/978-3-0348-9321-3_17

R. H. J. Gmelig Meyling¹⁰ &
P. R. Pfluger¹⁰

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 75))

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Abstract

We consider a closed subset Ω Ì ℝ² with a Polygonal boundary.

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References

CHUI, C.K., SCHUMAKER, L.L., and WANG, R.H., “on spaces of piecewise polynomials with boundary conditions”, II and III, in Second Edmonton Conference on Approximation Theory, AMS Vol.3, American Math.Soc., Providence(1985), pp. 51–80
Google Scholar
HEINDL, G., “Interpolation and approximation by piecewise quadratic C¹ -functions of two variables”, in Multivariate Approximation Theory, W. Schempp and K. Zeller, eds., Birkhauser, Basel(1979), pp. 146–161
Google Scholar
MORGAN J. and SCOTT R., “A nodal basis for C1 -Piecewise polynomials of degree n > 5”, Math.Comp.. 29 (1975), pp. 736–740
Google Scholar
MORGAN, J., and SCOTT, R., “The dimension of piecewise polynomials”, manuscript (1977), unpublished
Google Scholar
Numerical Algorithms Group, FORTRAN version, Mark 10, Oxford, England, 1984
Google Scholar
SCHUMAKER, L.L., “On the dimension of spaces of piecewise polynomials in two variables”, in Multivariate Approximation Theory, W. Schempp and K. Zeller, eds., Birkhauser, Basel(1979), pp. 396–412
Google Scholar
SCHUMAKER, L.L., “Bounds on the dimension of spaces of multivariate piecewise polynomials”, Rocky Mountain J. of Math Vo1. 14, No. 1, 1984, pp. 251–264
Article Google Scholar
SCHUMAKER, L.L., “On spaces of piecewise polynomials in two variables”, in Approximation Theory and spline functions, Proc. NATO Conf.. ed. S.P. Singh, Newfoundland, Canada, North-Holland, 1984
Google Scholar
SCHUMAKER, L.L., and Alfeld, P., private communication, 1984
Google Scholar

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Authors and Affiliations

Department of mathematics, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, The Netherlands
R. H. J. Gmelig Meyling & P. R. Pfluger

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R. H. J. Gmelig Meyling
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P. R. Pfluger
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Lehrstuhl für Mathematik I, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen, Germany
Walter Schempp
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen, Germany
Karl Zeller

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Meyling, R.H.J.G., Pfluger, P.R. (1985). On the Dimension of the Spline Space S ¹₂ (Δ) in Special Cases. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory III. International Series of Numerical Mathematics, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9321-3_17

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DOI: https://doi.org/10.1007/978-3-0348-9321-3_17
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9995-6
Online ISBN: 978-3-0348-9321-3
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