We apply multiresolution techniques to study the effective properties of boundary value problems. Conditions under which boundary values are preserved in the effective (`homogenized') formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic...

We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.

In this paper, we consider a wavelet based singularity-preserving regularization scheme for use in signal deconvolution problems. The inverse problem of finding solutions with singularities to discrete Fredholm integral equations of the first kind arises in many applied fields, e.g. in...

We propose multiresolution filter bank techniques to construct rotationally invariant moments. The multiresolution pyramid motivates a simple but efficient feature selection procedure based on a combination of a pruning algorithm, a new version of the Apriori mining techniques and partially...

Quasi-regression is a method of Monte Carlo approximation useful for global sensitivity analysis. This paper presents a new version, incorporating shrinkage parameters of the type used in wavelet approximation. As an example application, a black box function from machine learning is analyzed....

A numerical method for solving the nonlinear Volterra–Fredholm integral equations is presented. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties together with the Gaussian integration method are then utilized to...