Abstract
The classical interpolation problem is considered of estimating a function of one variable, f(.), given a number of function values f(xi), i=1,2,...,m. If a bound on ‖f(k)(.)‖∞ is given also, k≤m, then bounds on f(ζ) can be found for any ζ. A method of calculating the closest bounds is described, which is shown to be relevant to the problem of finding the interpolation formula whose error is bounded by the smallest possible multiple of ‖f(k)(.)‖∞, when ‖f(k)(.)‖∞ is unknown. This formula is identified and is called the optimal interpolation formula. The corresponding interpolating function is a spline of degree (k-1) with (m-k) knots, so it is very suitable for practical computation.
Keywords
- Interpolation Problem
- Lagrange Interpolation
- Interpolation Formula
- Optimal Interpolation
- Optimal Bound
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
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© 1976 Springer-Verlag
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Gaffney, P.W., Powell, M.J.D. (1976). Optimal interpolation. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080117
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DOI: https://doi.org/10.1007/BFb0080117
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07610-0
Online ISBN: 978-3-540-38129-7
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