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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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A method for solving classical smoothing problems with obstacles; pp. 197–204

(Full article in PDF format) doi: 10.3176/proc.2009.4.01


Authors

Evely Leetma

Abstract

We study how to reduce the smoothing problem with obstacles to the smoothing problem with weights. A system connecting deviations of the solution from given values and weights is established. An algorithm for solving this equation is proposed and illustrated by examples.

Keywords

numerical approximation, curve fitting, splines, multivariate natural splines, smoothing problems.

References

1. Ignatov , M. I. and Pevnyj , A. B. Natural Splines of Several Variables. Nauka , Leningrad. Otdel. , Leningrad , 1991 (in Russian).

2. Leetma , E. and Oja , P. A method of adding–removing knots for solving smoothing problems with obstacles. Eur. J. Oper. Res. , 2009 , 194 , 28–38.
doi:10.1016/j.ejor.2007.12.020

3. Kersey , S. N. On the problems of smoothing and near-interpolation. Math. Comp. , 2003 , 72 , 1873–1885.
doi:10.1090/S0025-5718-03-01523-0

4. Asmuss , S. , Budkina , N. , and Oja , P. On smoothing problems with weights and obstacles. Proc. Estonian Acad. Sci. Phys. Math. , 1997 , 46 , 262–272.

5. Bezhaev , A. Yu. and Vasilenko , V. A. Variational Theory of Splines. Kluwer Academic/Plenum Publishers , New York , 2001.

6. Kersey , S. N. Mixed interpolating–smoothing splines and the ν-spline. J. Math. Anal. Appl. , 2006 , 322 , 28–40.
doi:10.1016/j.jmaa.2005.07.007

7. Vershinin , V. V. , Zavyalov , Yu. S. , and Pavlov , N. N. Extremal Properties of Splines and the Smoothing Problem. Nauka , Sibirsk. Otdel. , Novosibirsk , 1988 (in Russian).
 
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Current Issue: Vol. 68, Issue 2 in Press, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December