Showing papers by "Aleksey Kudreyko published in 2010"
TL;DR: Periodic harmonic wavelets satisfy the properties of the multiresolution analysis and are proved to beperiodic wavelets of the second kind.
80 citations
TL;DR: In this paper, the application of the periodized harmonic wavelets for solution of integral equations and eigenvalue problems is discussed, and the solution is searched as a series of products of wavelet coefficients and wavelets.
Abstract: This article deals with the application of the periodized harmonic wavelets for solution of integral equations and eigenvalue problems. The solution is searched as a series of products of wavelet coefficients and wavelets. The absolute error for a general case of the wavelet approximation was analytically estimated.
31 citations
23 Mar 2010
TL;DR: The application of periodic wavelts as basis functions for solution of the Fredholm type integral equations for a degenerate kernel and multiscale solution of an integral equation for a non-degenerate kernel is examined.
Abstract: The paper deals with the application of periodic wavelts as basis functions for solution of the Fredholm type integral equations. We examine a special case for a degenerate kernel and show multiscale solution of an integral equation for a non-degenerate kernel. The benefits of the application of periodic harmonic wavelets are discussed. The approximation error of projection of solution on the space of periodized wavelets is analytically estimated.
2 citations