Previous |  Up |  Next

Article

Title: Interpolating and smoothing biquadratic spline (English)
Author: Kučera, Radek
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
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
.
Date available: 2009-09-22T17:48:42Z
Last updated: 2012-05-06
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
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
.

Files

Files Size Format View
AplMat_40-1995-5_1.pdf 1.439Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo