Anton A. Makarov's scientific contributions

Publications (3)

Article
Piecewise continuous spline of Lagrange type are constructed. An embedding of spline spaces is established for arbitrary refinement of grids. The system of biorthogonal linear functionals to splines is constructed. Wavelet decompositions and decomposition and reconstruction algorithms in the case of an infinite flow for a grid on an open interval a...
Article
The aim of the paper is construction of calibration relations in the case of class of coordinate non-polynomial splines connected with refinement of grids. An embed\-ding of spline spaces is established for arbitrary refinement of grids. The reconstruction matrixes in the case of a grid on an open interval and a grid on a segment are constructed. T...
Article
The goal of this paper is to obtain a wavelet decomposition (wavelet renement) of the chain of embedded spaces of splines for an arbitrary renement of a nonuniform grid, and to derive the corresponding decomposition and reconstruction formulas, to construct wavelet decompositions and decomposition and reconstruction algorithms in the case of an inn...

Citations

... For nonuniform meshes, of principal importance is the problem of constructing the calibration relations, which generalize the classical scaling equations for uniform meshes. In earlier papers (see, e.g., [1][2][3]), spline-wavelet decompositions were constructed in the cases where nodes were consecutively removed or added. The same approach allows one to remove groups of adjacent nodes, which are referred to as nests [4], or to perform a single local coarsening of a nonuniform mesh [5,6]. ...