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Cubic splines with minimal norm. (English) Zbl 1090.65012
The author considers cubic splines which minimize some norms (or functionals) on the class of interpolatory cubic splines. The cases of classical cubic splines with defect one and of Hermite \(C^1\) splines with spline knots different from the points of interpolation are discussed.

MSC:
65D05 Numerical interpolation
65D07 Numerical computation using splines
41A15 Spline approximation
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References:
[1] A. Bjorck: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, 1996.
[2] C. Boor: A Practical Guide to Splines. Springer-Verlag, New York-Heidelberg-Berlin, 1978. · Zbl 0406.41003
[3] L. Brugnano, D. Trigiante: Solving Differential Equations by Multistep. Initial and Boundary Value Methods. Gordon and Breach, London, 1998. · Zbl 0934.65074
[4] R. Fletcher: Practical Methods of Optimization. Wiley, Chichester, 1993. · Zbl 0905.65002
[5] J. Kobza: Splajny. Textbook. VUP, Olomouc, 1993.
[6] J. Kobza: Computing solutions of linear difference equations. Proceedings of the XIIIth Summer School Software and Algorithms of Numerical Mathematics, Nečtiny 1999, I. Marek (ed.), University of West Bohemia, Plzeň, 1999, pp. 157-172.
[7] J. S. Zavjalov, B. I. Kvasov and V. L. Miroschnichenko: Methods of Spline Functions. Nauka, Moscow, 1980.
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