| Title:
|
Interpolating and smoothing biquadratic spline (English) |
| Author:
|
Kučera, Radek |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
5 |
| Year:
|
1995 |
| Pages:
|
339-356 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and their bases are given by the so-called fundamental splines. (English) |
| Keyword:
|
quadratic spline |
| Keyword:
|
biquadratic spline |
| Keyword:
|
derivative |
| Keyword:
|
interpolation |
| Keyword:
|
smoothing |
| MSC:
|
41A05 |
| MSC:
|
41A15 |
| MSC:
|
65D05 |
| MSC:
|
65D07 |
| idZBL:
|
Zbl 0835.41016 |
| idMR:
|
MR1342364 |
| DOI:
|
10.21136/AM.1995.134298 |
| . |
| Date available:
|
2009-09-22T17:48:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134298 |
| . |
| Reference:
|
[ANW67] J.H. Ahlberg, E.N. Nilson, J.L. Walsh: The Theory of Splines and their Applications.Academic Press, New York-London, 1967. MR 0239327 |
| Reference:
|
[B62] C. de Boor: Bicubic Spline Interpolation.J. Math. and Physics, 41 (1962), 212–218. Zbl 0108.27103, MR 0158512, 10.1002/sapm1962411212 |
| Reference:
|
[B78] C. de Boor: A Practical Guide to Splines.Springer Verlag, New York, 1978. Zbl 0406.41003, MR 0507062 |
| Reference:
|
[EMM89] S. Ewald, H. Mühlig, B. Mulansky: Bivariate Interpolating and Smoothing Tensor Product Splines.Proceeding ISAM, Berlin, 1989, pp. 59–68. |
| Reference:
|
[I75] A. Imamov: About some Properties of Multivariate Splines.Vyčislitelnye sistemy (Novosibirsk) 65 (1975), 68–73. (Russian) MR 0460978 |
| Reference:
|
[K87] J. Kobza: An Algorithm for Biquadratic Spline.Appl. Math. 32 (1987), no. 5, 401–413. MR 0909546 |
| Reference:
|
[K92] J. Kobza: Quadratic Splines Smoothing the First Derivatives.Appl. Math. 37 (1992), no. 2, 149–156. Zbl 0757.65006, MR 1149164 |
| Reference:
|
[KK93] J. Kobza, R. Kučera: Fundamental Quadratic Splines and Applications.Acta UPO 32 (1993), 81–98. MR 1273172 |
| Reference:
|
[HS86] J. Kobza, D. Zápalka: Natural and Smoothing Quadratic Spline.Appl. Math. 36 (1991), no. 3, 187–204. MR 1109124 |
| Reference:
|
[N89] G. Nürnberger: Approximation by Spline Function.Springer Verlag, New York, 1989. MR 1022194 |
| Reference:
|
[ZKM80] J.S. Zavjalov, B.I. Kvasov, V.L. Miroshnichenko: Methods of Spline Functions.Nauka, Moscow, 1980. (Russian) MR 0614595 |
| . |
