Quadratic splines smoothing the first derivatives

Jiří Kobza

Applications of Mathematics (1992)

  • Volume: 37, Issue: 2, page 149-156
  • ISSN: 0862-7940

Abstract

top
The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights w i and smoothing parameter α , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter α is mentioned.

How to cite

top

Kobza, Jiří. "Quadratic splines smoothing the first derivatives." Applications of Mathematics 37.2 (1992): 149-156. <http://eudml.org/doc/15706>.

@article{Kobza1992,
abstract = {The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights $w_i$ and smoothing parameter $\alpha $, is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter $\alpha $ is mentioned.},
author = {Kobza, Jiří},
journal = {Applications of Mathematics},
keywords = {interpolation; smoothing; quadratic spline; interpolation; smoothing; quadratic spline},
language = {eng},
number = {2},
pages = {149-156},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quadratic splines smoothing the first derivatives},
url = {http://eudml.org/doc/15706},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Kobza, Jiří
TI - Quadratic splines smoothing the first derivatives
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 2
SP - 149
EP - 156
AB - The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights $w_i$ and smoothing parameter $\alpha $, is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter $\alpha $ is mentioned.
LA - eng
KW - interpolation; smoothing; quadratic spline; interpolation; smoothing; quadratic spline
UR - http://eudml.org/doc/15706
ER -

References

top
  1. Ahlberg J. H., Nilson E. N., Walsh J. L., The Theory of Splines and Their Aplications, Academic Press, N.Y., 1967. (1967) MR0239327
  2. de Boor C., A Practical Guide to Splines, Springer Verlag, N.Y., 1978. (1978) Zbl0406.41003MR0507062
  3. Kobza J., An algorithm for parabolic splines, Acta UPO, FRN 88 (1987), 169-185. (1987) MR1033338
  4. Kobza J., Quadratic splines interpolating the first derivatives, Acta UPO, FRN 100 (1991), 219-233. (1991) MR1166439
  5. Kobza J., Zápalka D., Natural and smoothing quadratic spline, Applications of Mathematics 36 no. 3 (1991), 187-204. (1991) MR1109124
  6. Laurent P.-J., Approximation et Optimization, Hermann, Paris, 1972. (1972) MR0467080
  7. Sallam S., Tarazi M.N., Quadratic spline interpolation on uniform meshes, In Splines in Numerical Analysis (Schmidt J.W., Spaeth H., eds.), Akademie-Verlag, Berlin, 1989, pp. 145-150. (1989) Zbl0677.65010MR1004259
  8. Schultz M., Spline Analysis, Prentice-Hall, Englewood Cliffs, N.Y., 1973. (1973) Zbl0333.41009MR0362832
  9. Vasilenko V.A., Spline Functions: Theory, Algorithms, Programs, Nauka, SO, Novosibirsk, 1983. (In Russian.) (1983) Zbl0529.41013MR0721970

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.