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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:
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


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