On the Convergence of Some Cubic Spline Interpolation Schemes

Cubic spline interpolation schemes which require no derivative information at the end points are of great practical importance and have been included in several general purpose software libraries. In this paper optimal order error estimates are developed for three popular schemes of this "deriv...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 23; no. 4; pp. 903 - 912
Main Author Beatson, R. K.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1986
Subjects
Approximation
Cubic polynomials
Error bounds
Estimates
Exact sciences and technology
Interpolation
Knots
Linear systems
Mathematical functions
Mathematical vectors
Mathematics
Matrices
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Taylor series
Interpolation
Approximation
Error estimation
Cubic spline
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Summary:Cubic spline interpolation schemes which require no derivative information at the end points are of great practical importance and have been included in several general purpose software libraries. In this paper optimal order error estimates are developed for three popular schemes of this "derivative free" type. The approximation of$C^1 \lbrack a, b \rbrack\C^2 \lbrack a, b \rbrack$functions by any such "derivative free" method that reproduces cubics, necessarily displays some dependence on the local mesh ratio. However, for the spline interpolants studied here this dependence is restricted to the first and last subintervals.
ISSN:0036-1429
1095-7170
DOI:10.1137/0723058