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This article is cited in 1 scientific paper (total in 1 paper)
On an algorithm of bilateral restrictions smoothing with spline
A. I. Rozhenkoa, E. A. Fedorovb a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia
b ООО "Data Ist", 2/2 Lavrentiev pr., Novosibirsk, 630090, Russia
Abstract:
In this paper, the problem of constructing a spline $\sigma$ in the Hilbert space satisfying bilateral restrictions $z^-\le A\sigma\le z^+$ with a linear operator $A$ and minimizing a squared Hilbert seminorm is studied. A solution to this problem could be obtained with the convex programming iterative methods, in particular, with the gradient projection method. A modification of the gradient projection method allowing one to reveal a set of active restrictions in a smaller number of iterations is offered. The efficiency of the modification proposed is shown on the problem of approximation with a pseudo-linear bivariate spline.
Key words:
smoothing, spline, Hilbert space, convex programming, reproducing mapping, radial basis function.
Received: 22.11.2015 Revised: 11.02.2016
Citation:
A. I. Rozhenko, E. A. Fedorov, “On an algorithm of bilateral restrictions smoothing with spline”, Sib. Zh. Vychisl. Mat., 19:3 (2016), 331–342; Num. Anal. Appl., 9:3 (2016), 257–266
Linking options:
https://www.mathnet.ru/eng/sjvm621 https://www.mathnet.ru/eng/sjvm/v19/i3/p331
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Abstract page: | 179 | Full-text PDF : | 34 | References: | 33 | First page: | 8 |
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