About calculation of the Hankel transform using preliminary wavelet transform.
Accelerating the convergence of trigonometric series
A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.
Adaptive prediction of stock exchange indices by state space wavelet networks
The paper considers the forecasting of the Warsaw Stock Exchange price index WIG20 by applying a state space wavelet network model of the index price. The approach can be applied to the development of tools for predicting changes of other economic indicators, especially stock exchange indices. The paper presents a general state space wavelet network model and the underlying principles. The model is applied to produce one session ahead and five sessions ahead adaptive predictors of the WIG20 index...
Adaptive wavelet methods for saddle point problems
Adaptive wavelet methods for saddle point problems
Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....
Algebraic properties of refinable sets.
Algebraic theory of fast mixed-radix transforms. I. Generalized Kronecker product of matrices
Algebraic theory of fast mixed-radix transforms. II. Computational complexity and applications
An algebraic construction of discrete wavelet transforms
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
An analytical method for calculation of integrals appearing in approximate solutions of deformable body mechanics
An operational Haar wavelet method for solving fractional Volterra integral equations
A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations.
Application of the irregular spectra to the harmonic analysis of empirical functions
Approximate multiplication in adaptive wavelet methods
Cohen, Dahmen and DeVore designed in [Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 2001, 70(233), 27–75] and [Adaptive wavelet methods II¶beyond the elliptic case, Found. Comput. Math., 2002, 2(3), 203–245] a general concept for solving operator equations. Its essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l 2-problem, finding the convergent iteration process for the l 2-problem and finally...
Approximation in L... Sobolev Spaces on the 2-Sphere by Quasi-Interpolation.
Approximation properties of wavelets and relations among scaling moments II
A new orthonormality condition for scaling functions is derived. This condition shows a close connection between orthonormality and relations among discrete scaling moments. This new condition in connection with certain approximation properties of scaling functions enables to prove new relations among discrete scaling moments and consequently the same relations for continuous scaling moments.
Attenuation Factors in Multivariate Fourier Analysis.
Attenuation Factors in Practical Fourier Analysis.
Barycentric Formulas for Interpolating Trigonometric Polynomials and their Conjugates.
Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind.