ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
A method for solving classical smoothing problems with obstacles; pp. 197–204
PDF | doi: 10.3176/proc.2009.4.01

Author
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.
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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