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Numerical Analysis and Applications

2016 year, number 3

On an algorithm of bilateral restrictions smoothing with spline

Aleksandr Iosifovich Rozhenko1, Egor A. Fedorov2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva, 6, Novosibirsk, 630090, Russia
2ООО В«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


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.