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On optimal approximation

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Part of the Lecture Notes in Mathematics book series (LNM,volume 501)

Abstract

This note presents a new instance of spline approximation in which the observation of a function is its value on an interior contour or hypersurface and the coobservation is its gradient. There follow three comments relevant to the application of the theory of optimal approximation.

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References

  1. Sard, A.: Optimal approximation. J. Functional Analysis 1(1967), 222–244 and 2(1968), 368–369.

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  2. Sard, A.: Approximation based on nonscalar observations. J. Approximation Theory 8(1973), 315–334.

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  3. Sard, A.: Instances of generalized splines. In K. Böhmer, G. Meinardus, W. Schempp, Editors: Spline-Funktionen. Bibliographisches Institut, Mannheim, Wien, Zürich. 215–241, 1974.

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  4. Delvos, F.-J. and W. Schempp: Sard's method and the theory of spline systems. J. Approximation Theory 14(1975), 230–243.

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  5. Delvos, F.-J.: On surface interpolation. To appear in J. Approximation Theory.

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  6. Delvos, F.-J. and Posdorf, H.: On optimal tensor product approximation. To appear in J. Approximation Theory.

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© 1976 Springer-Verlag

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Sard, A. (1976). On optimal approximation. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079750

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  • DOI: https://doi.org/10.1007/BFb0079750

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07543-1

  • Online ISBN: 978-3-540-38073-3

  • eBook Packages: Springer Book Archive