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Abstract

Let (xk) be a bi-infinite knot sequence for which the mesh ratio is smaller than some exponential order (in particular, the local mesh ratio must be finite, but the global mesh ratio may be infinite). Let p be a non-negative real number, and (yk) a data sequence for which yk = 0(|xk|ρ) as k ∈ ± ∞. We prove the existence and uniqueness of a spline function of any previously specified odd degree, with knots (xk), which interpolates (yk) (that is, S(xk) = yk for all k) and which is dominated by exactly the same power, namely S(t) = 0 (|t|ρ) as t → ±∞. We may replace 0 by o throughout. We also obtain a series representation for S(·) in terms of (yk) and of a sequence of “fundamental splines” Lk(·) which decay exponentially near ±∞.

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References

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© 1984 Springer Basel AG

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Jakimovski, A., Russell, D.C., Stieglitz, M. (1984). Spline Interpolation of Power-Dominated Data. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_36

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  • DOI: https://doi.org/10.1007/978-3-0348-5432-0_36

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5434-4

  • Online ISBN: 978-3-0348-5432-0

  • eBook Packages: Springer Book Archive

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