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Introduction: The Problem to be Solved

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Abstract

In practice, a function of interest is only given pointwise, that is, there exists a point grid \(\{{x{}_{j}\}}_{j=1,\ldots, G}\) where \(\{F{({x}_{j})\}}_{j=1,\ldots, G}\) is known.

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Notes

  1. 1.

    This is certainly a simplification. For further details, see [58, 98, 145, 171, 202].

  2. 2.

    For instance, the Earth gravity model EGM96 (see [110, 203]) uses more than 130,000 basis functions, and EGM 2008 (see [146, 204]) even has more then 4,000,000 basis functions.

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    Volker Michel

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Michel, V. (2013). Introduction: The Problem to be Solved. In: Lectures on Constructive Approximation. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8403-7_1

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