Which cubic spline should one use?

The aim of this paper is to provide a quantitative comparison of eight different $C^1 $ and $C^2 $ cubic spline interpolation schemes. The $C^1 $ schemes discussed are local while the $C^2 $ ones are global. In practice cubic splines are often used when the smoothness of the function being interpola...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 13; no. 4; pp. 1009 - 1024
Main Authors BEATSON, R. K, CHACKO, E
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.07.1992
Subjects
Applied mathematics
Approximation
Estimates
Exact sciences and technology
Knots
Mathematics
Methods
Norms
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Interpolation
Grid pattern
Error estimation
Comparative study
Cubic spline
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Summary:The aim of this paper is to provide a quantitative comparison of eight different $C^1 $ and $C^2 $ cubic spline interpolation schemes. The $C^1 $ schemes discussed are local while the $C^2 $ ones are global. In practice cubic splines are often used when the smoothness of the function being interpolated/approximated is unknown. Also, it is often necessary, or advantageous, to use a nonuniform mesh. Therefore performance over a variety of smoothness classes, using uniform and also several thousand random meshes, is compared. The performance criteria used are the quantitative ones of exact operator and derived operator norms and best possible pointwise error estimates.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0913059