Geodesic
Abstract splines with the tension as the functions of parameters in energy operator
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 301-311 
V. A. Vasilenko; A. V. Elyseev. Abstract splines with the tension as the functions of parameters in energy operator. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 301-311. http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the framework of general optimization of energy functional in variational spline interpolation approach we consider the multiparametric family of energy operators linear depending on parameters (it corresponds to abstract splines with the tension). Our main result consists in the representation of this kind of spline as the function of parameters in energy operator. It provides the explicit calculation of various criteria functions for forthcoming choice of optimal parameters.

[1] Bezhaev A. Yu., Vasilenko V. A., Variational Spline Theory, Bull. of the Novosibirsk Computing Center, Num. Anal., 3, Special, NCC Publisher, Novosibirsk, 1993

[2] Vasilenko V. A., “Optimization of energy functional for variational splines”, Bull. of the Novosibirsk Computing Center, Num. Anal., 7, NCC Publisher, Novosibirsk, 1996, 101–107

[3] Biblioteka programm LIDA-3 po approksimatsii funktsii i tsifrovoi filtratsii signalov i izobrazhenii. Chast I. Approksimatsiya, Izd. VTs SO AN SSSR, Novosibirsk, 1987