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Quasi-Interpolation on Irregular Points

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Approximation and Computation: A Festschrift in Honor of Walter Gautschi

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 119))

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Abstract

A quasi-interpolant is an operator L having the form

$$Lf = \sum\limits_{i = 1}^\infty {f\left( {{y_i}} \right){g_i}} .$$
(1.1)

The points y i are called “nodes”; they are prescribed in ℝn. The entities g i are prescribed functions from ℝn to ℝ. The case of irregularly situated nodes is of particular interest. We investigate the question of how to select the “base functions” g i in order to obtain favorable estimates of ∥Lf - f∥.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    E. W. Cheney & Junjiang Lei

Authors
  1. E. W. Cheney
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  2. Junjiang Lei
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Editor information

Editors and Affiliations

  1. Département d’informatique et de recherche opérationnelle, Université de Montréal, Succursale “Centre-Ville”, C.P. 6128, H3C 3J7, Montréal, Québec, Canada

    R. V. M. Zahar

Additional information

Dedicated to Walter Gautschi on the occasion of his 65th birthday

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© 1994 Birkhäuser

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Cheney, E.W., Lei, J. (1994). Quasi-Interpolation on Irregular Points. In: Zahar, R.V.M. (eds) Approximation and Computation: A Festschrift in Honor of Walter Gautschi. ISNM International Series of Numerical Mathematics, vol 119. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-7415-2_8

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  • DOI: https://doi.org/10.1007/978-1-4684-7415-2_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4684-7417-6

  • Online ISBN: 978-1-4684-7415-2

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