Error estimates for interpolation with piecewise exponential splines of order two and four

Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended to a natural class of piecewise exponential splines which are appearing in the construction of multivariate polysplines....

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2021-08, Vol.391, p.113464, Article 113464
Main Authors: Kounchev, O., Render, H.
Format: Article
Language:English
Subjects:
Approximation rate
Error estimate
Exponential splines
Interpolation [formula omitted]splines
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Summary:Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended to a natural class of piecewise exponential splines which are appearing in the construction of multivariate polysplines. The error estimates are derived in an inductive way using error estimates for the interpolation of a smooth function by exponential splines of order two.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113464