On an algorithm of bilateral restrictions smoothing with spline

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.