| Title:
|
Natural and smoothing quadratic spline. (An elementary approach) (English) |
| Author:
|
Kobza, Jiří |
| Author:
|
Zápalka, Dušan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
187-204 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For quadratic spine interpolating local integrals (mean-values) on a given mesh the conditions of existence and uniqueness, construction under various boundary conditions and other properties are studied. The extremal property of such's spline allows us to present an elementary construction and an algorithm for computing needed parameters of such quadratic spline smoothing given mean-values. Examples are given illustrating the results. (English) |
| Keyword:
|
spline functions |
| Keyword:
|
quadratic spline |
| Keyword:
|
interpolation |
| Keyword:
|
smoothing by splines |
| Keyword:
|
histosplines |
| Keyword:
|
parabolic spline |
| Keyword:
|
cubic spline interpolation |
| Keyword:
|
natural spline interpolation |
| MSC:
|
41A15 |
| MSC:
|
65D05 |
| MSC:
|
65D07 |
| idZBL:
|
Zbl 0731.65006 |
| idMR:
|
MR1109124 |
| DOI:
|
10.21136/AM.1991.104459 |
| . |
| Date available:
|
2008-05-20T18:41:38Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104459 |
| . |
| Reference:
|
[1] J. H. Ahlberg E. N. Nilson J. L. Walsh: The Theory of Splines and Their Applications.Acad. Press, New York 1967 (Russian translation, Moscow, Mir 1972). MR 0239327 |
| Reference:
|
[2] C. de Boor: A Practical Guide to Splines.New York, Springer-Verlag 1978 (Russian translation, Moscow, Sov. radio 1985). Zbl 0406.41003, MR 0507062 |
| Reference:
|
[3] J. Kobza: An algorithm for biparabolic spline.Aplikace matematiky 32 (1987), 401-413. Zbl 0635.65006, MR 0909546 |
| Reference:
|
J. Kobza: Some properties of interpolating quadratic splines.Acta UPO, FRN, Vol. 97 (1990), Math. XXIV, 45-63. MR 1144830 |
| Reference:
|
[4] P.-J. Laurent: Approximation et optimization.Paris, Hermann 1972 (Russian translation, Moscow, Mir. 1975). MR 0467080 |
| Reference:
|
[5] В. Л. Макаров В. В. Хлобыстов: Сплайн-аппроксимация функций.Москва, Высшая школа 1983. Zbl 1229.47001 |
| Reference:
|
[6] I. J. Schoenberg: Splines and histograms.In: Spline Functions and Approximation Theory (Meir, Sharma - eds.), Basel, Birkhäuser Verlag (1973), 277-327. Zbl 0274.41004, MR 0372477 |
| Reference:
|
[7] M. H. Schultz: Spline Analysis.Englewood Cliffs, Prentice-Hall 1973. Zbl 0333.41009, MR 0362832 |
| Reference:
|
[8] С. Б. Стечкин Ю. H. Субботин: Сплайны в вычислительной математике.Москва, Наука 1976. Zbl 1226.05083 |
| Reference:
|
[9] В. А. Василенко: Сплайн-функции. Теория, алгоритмы, программы.Новосибирск, Наука (СО), 1983. Zbl 1171.53341 |
| Reference:
|
[10] В. С. Завьялов Б. И. Квасов В. Л. Мирошниченко: Методы сплайн-функций.Москва, Наука 1980. Zbl 1229.60003 |
| . |
