Natural and smoothing quadratic spline. (An elementary approach)

Jiří Kobza; Dušan Zápalka

Applications of Mathematics (1991)

  • Volume: 36, Issue: 3, page 187-204
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Kobza, Jiří, and Zápalka, Dušan. "Natural and smoothing quadratic spline. (An elementary approach)." Applications of Mathematics 36.3 (1991): 187-204. <http://eudml.org/doc/15673>.

@article{Kobza1991,
abstract = {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.},
author = {Kobza, Jiří, Zápalka, Dušan},
journal = {Applications of Mathematics},
keywords = {spline functions; quadratic spline; interpolation; smoothing by splines; histosplines; parabolic spline; cubic spline interpolation; natural spline interpolation; smoothing quadratic spline; histosplines; parabolic spline; interpolation; cubic spline interpolation; natural spline interpolation},
language = {eng},
number = {3},
pages = {187-204},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Natural and smoothing quadratic spline. (An elementary approach)},
url = {http://eudml.org/doc/15673},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Kobza, Jiří
AU - Zápalka, Dušan
TI - Natural and smoothing quadratic spline. (An elementary approach)
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 3
SP - 187
EP - 204
AB - 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.
LA - eng
KW - spline functions; quadratic spline; interpolation; smoothing by splines; histosplines; parabolic spline; cubic spline interpolation; natural spline interpolation; smoothing quadratic spline; histosplines; parabolic spline; interpolation; cubic spline interpolation; natural spline interpolation
UR - http://eudml.org/doc/15673
ER -

References

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  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). (1967) MR0239327
  2. C. de Boor, A Practical Guide to Splines, New York, Springer-Verlag 1978 (Russian translation, Moscow, Sov. radio 1985). (1978) Zbl0406.41003MR0507062
  3. J. Kobza, An algorithm for biparabolic spline, Aplikace matematiky 32 (1987), 401-413. (1987) Zbl0635.65006MR0909546
  4. J. Kobza, Some properties of interpolating quadratic splines, Acta UPO, FRN, Vol. 97 (1990), Math. XXIV, 45-63. (1990) MR1144830
  5. P.-J. Laurent, Approximation et optimization, Paris, Hermann 1972 (Russian translation, Moscow, Mir. 1975). (1972) MR0467080
  6. В. Л. Макаров В. В. Хлобыстов, Сплайн-аппроксимация функций, Москва, Высшая школа 1983. (1983) Zbl1229.47001
  7. I. J. Schoenberg, Splines and histograms, In: Spline Functions and Approximation Theory (Meir, Sharma - eds.), Basel, Birkhäuser Verlag (1973), 277-327. (1973) Zbl0274.41004MR0372477
  8. M. H. Schultz, Spline Analysis, Englewood Cliffs, Prentice-Hall 1973. (1973) Zbl0333.41009MR0362832
  9. С. Б. Стечкин Ю. H. Субботин, Сплайны в вычислительной математике, Москва, Наука 1976. (1976) Zbl1226.05083
  10. В. А. Василенко, Сплайн-функции. Теория, алгоритмы, программы, Новосибирск, Наука (СО), 1983. (1983) Zbl1171.53341
  11. В. С. Завьялов Б. И. Квасов В. Л. Мирошниченко, Методы сплайн-функций, Москва, Наука 1980. (1980) Zbl1229.60003

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