Abstract
Multivariate smooth splines on nonuniform rectangular grids are investigated. A general theory of Boolean methods is developed in such a way that it can be applied to noncommutative operators. Based on this theory, an explicit quasi-interpolant is constructed so that it gives rise to an efficient scheme of approximation by multivariate smooth splines. This scheme is shown to achieve the optimal rate of approximation.
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Dedicated to the memory of Lothar Collatz
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© 1992 Springer Basel AG
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Jia, RQ. (1992). Approximation by Multivariate Splines: an Application of Boolean Methods. In: Braess, D., Schumaker, L.L. (eds) Numerical Methods in Approximation Theory, Vol. 9. ISNM 105: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 105. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8619-2_7
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DOI: https://doi.org/10.1007/978-3-0348-8619-2_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9702-0
Online ISBN: 978-3-0348-8619-2
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