| Title:
|
Quadratic splines smoothing the first derivatives (English) |
| Author:
|
Kobza, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
149-156 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
interpolation |
| Keyword:
|
smoothing |
| Keyword:
|
quadratic spline |
| MSC:
|
41A15 |
| MSC:
|
65D05 |
| MSC:
|
65D07 |
| MSC:
|
65D10 |
| idZBL:
|
Zbl 0757.65006 |
| idMR:
|
MR1149164 |
| DOI:
|
10.21136/AM.1992.104498 |
| . |
| Date available:
|
2008-05-20T18:43:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104498 |
| . |
| Reference:
|
[1] Ahlberg J. H., Nilson E. N., Walsh J. L.: The Theory of Splines and Their Aplications.Academic Press, N.Y., 1967. MR 0239327 |
| Reference:
|
[2] de Boor C.: A Practical Guide to Splines.Springer Verlag, N.Y., 1978. Zbl 0406.41003, MR 0507062 |
| Reference:
|
[3] Kobza J.: An algorithm for parabolic splines.Acta UPO, FRN 88 (1987), 169-185. MR 1033338 |
| Reference:
|
[4] Kobza J.: Quadratic splines interpolating the first derivatives.Acta UPO, FRN 100 (1991), 219-233. MR 1166439 |
| Reference:
|
[5] Kobza J., Zápalka D.: Natural and smoothing quadratic spline.Applications of Mathematics 36 no. 3 (1991), 187-204. MR 1109124 |
| Reference:
|
[6] Laurent P.-J.: Approximation et Optimization.Hermann, Paris, 1972. MR 0467080 |
| Reference:
|
[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. Zbl 0677.65010, MR 1004259 |
| Reference:
|
[8] Schultz M.: Spline Analysis.Prentice-Hall, Englewood Cliffs, N.Y., 1973. Zbl 0333.41009, MR 0362832 |
| Reference:
|
[9] Vasilenko V.A.: Spline Functions: Theory, Algorithms, Programs.Nauka, SO, Novosibirsk, 1983. (In Russian.) Zbl 0529.41013, MR 0721970 |
| . |
