Cubic splines with minimal norm

Jiří Kobza

Applications of Mathematics (2002)

  • Volume: 47, Issue: 3, page 285-295
  • ISSN: 0862-7940

Abstract

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Natural cubic interpolatory splines are known to have a minimal L 2 -norm of its second derivative on the C 2 (or W 2 2 ) class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite C 1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.

How to cite

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Kobza, Jiří. "Cubic splines with minimal norm." Applications of Mathematics 47.3 (2002): 285-295. <http://eudml.org/doc/33116>.

@article{Kobza2002,
abstract = {Natural cubic interpolatory splines are known to have a minimal $L_2$-norm of its second derivative on the $C^2$ (or $W^2_2)$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^1$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.},
author = {Kobza, Jiří},
journal = {Applications of Mathematics},
keywords = {cubic interpolatory spline; minimal norm interpolation; cubic interpolatory spline; minimal norm interpolation},
language = {eng},
number = {3},
pages = {285-295},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cubic splines with minimal norm},
url = {http://eudml.org/doc/33116},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Kobza, Jiří
TI - Cubic splines with minimal norm
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 285
EP - 295
AB - Natural cubic interpolatory splines are known to have a minimal $L_2$-norm of its second derivative on the $C^2$ (or $W^2_2)$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^1$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.
LA - eng
KW - cubic interpolatory spline; minimal norm interpolation; cubic interpolatory spline; minimal norm interpolation
UR - http://eudml.org/doc/33116
ER -

References

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  1. Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996. (1996) MR1386889
  2. A Practical Guide to Splines, Springer-Verlag, New York-Heidelberg-Berlin, 1978. (1978) Zbl0406.41003MR0507062
  3. Solving Differential Equations by Multistep. Initial and Boundary Value Methods, Gordon and Breach, London, 1998. (1998) MR1673796
  4. Practical Methods of Optimization, Wiley, Chichester, 1993. (1993) MR1867781
  5. Splajny. Textbook, VUP, Olomouc, 1993. (Czech) (1993) 
  6. Computing solutions of linear difference equations, In: 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. (1999) 
  7. Methods of Spline Functions, Nauka, Moscow, 1980. (Russian) (1980) MR0614595

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