On an algorithm of bilateral restrictions smoothing with spline
Aleksandr Iosifovich Rozhenko1, Egor A. Fedorov2
a:2:{s:4:"TYPE";s:4:"HTML";s:4:"TEXT";s:231:"1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva, 6, Novosibirsk, 630090, Russia
2ООО «Data Ist», pr. Acad. Lavrentieva, 22, Novosibirsk, 630090, Russia";}
Keywords: сглаживание, сплайн, гильбертово пространство, выпуклое программирование, воспроизводящее отображение, радиальная базисная функция, smoothing, spline, Hilbert space, convex programming, reproducing mapping, radial basis function
Abstract
In this paper, the problem of constructing a spline σ in the Hilbert space satisfying bilateral restrictions z- ≤ A σ ≤ 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.
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