Geodesic
On orthogonal decomposition of space in spline-fitting problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 3, pp. 291-297.

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A special orthogonal decomposition of a basic space for an abstract quasi-spline-fitting problem is proposed. Using this decomposition, a theorem on representation of smoothing quasi-spline $\sigma_{\alpha}$ is proved. Exact in order convergence estimates of $\sigma_{\alpha}$ to the limit quasi-splines $\sigma_0$ and $\sigma_{\infty}$ are obtained. The monotony and the upper convexity of the function $\psi^{-1}(\beta)$, used in the algorithm of selection of the smoothing parameter $\alpha$ by the residual criterion, are proved. 
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A. I. Rozhenko. On orthogonal decomposition of space in spline-fitting problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 3, pp. 291-297. http://geodesic.mathdoc.fr/item/SJVM_2003_6_3_a6/

[1] Reinsch C. H., “Smoothing by spline functions”, Numer. Math., 10:3 (1967), 177–183 | DOI | MR | Zbl

[2] Vasilenko V. A., Splain-funktsii: teoriya, algoritmy, programmy, Nauka. Sib. otd-nie, Novosibirsk, 1983 | MR

[3] Morozov V. A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach, Nauka, M., 1987 | MR

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

[5] Gordonova V. I., Morozov V. A., “Chislennye algoritmy vybora parametra v metode regulyarizatsii”, Zhurn. vychisl. matematiki i mat. fiziki, 13:3 (1973), 539–545 | MR

[6] Bezhaev A. Yu., “Metody rascheta optimalnogo parametra sglazhivaniya pri postroenii variatsionnogo splaina”, Variatsionnye metody v zadachakh chislennogo analiza, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1991, 3–26

[7] Rozhenko A. I., “On optimal choice of spline-smoothing parameter”, Bull. of the Novosibirsk Computing Center. Series: Num. Anal., 7, NCC Publisher, Novosibirsk, 1996, 79–86

[8] Rozhenko A. I., Abstraktnaya teoriya splainov, Izd. tsentr NGU, Novosibirsk, 1999

[9] Loran P.-Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975