Geodesic
On some properties of the projection operator for a class of stabilization algorithms
Numerical methods and programming, Tome 19 (2018) no. 4, pp. 431-438.

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The projection operator $Q[a]$ acting from the linear space of the functions $a (x) \in \mathrm{span} \{\sin i x,\; i \ge 1\}$ given on the segment $[0,\pi]$ onto the subspace of the functions $\tilde a(x) \in \mathrm{span} \{\sin i x,\; i > i_0\}$ is studied theoretically and numerically. The corresponding projection is performed along the subspace of the functions $l(x) \in \mathrm{span} \{{ \overline{\mathrm{ sin}}}\ i x , \; i=1,\ldots, i_0\}$, where ${ \overline{\mathrm{sin}}}\ i x = \chi_\delta (x) \sin i x$ is the characteristic function $\chi_{\delta} (x)$ of the interval $[0,\delta)$. The obtained results are used to solve the problem of stabilization with respect to the initial data of solutions to the model nonstationary equations.
Keywords: numerical methods, projection operator, stabilization. 
@article{VMP_2018_19_4_a9,
     author = {A. A. Kornev},
     title = {On some properties of the projection operator for a class of stabilization algorithms},
     journal = {Numerical methods and programming},
     pages = {431--438},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a9/}
}
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A. A. Kornev. On some properties of the projection operator for a class of stabilization algorithms. Numerical methods and programming, Tome 19 (2018) no. 4, pp. 431-438. http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a9/