We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...

Adaptive Solution of Partial Differential Equations in Multiwavelet Bases B. Alpert,∗,1 G. Beylkin,†,2 D. Gines,† and L. Vozovoi‡,3,4,5 ∗National Institute of Standards and Technology, Boulder, Colorado 80305-3328; †Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526; and ‡School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel E-mail: al...

| In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttlter for the lterbank determined by the underlying multiwavelets. We give a construction for orthogonal (paraunitary) FIR pre-lters that preserve the approximation order of a g...

Unshifted and shifted multiscaling functions are used as mathematical models for curve fitting of irregularly sampled data. This pre-processing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In the case of low resolution it is more accurate than numerical integration and cheaper than matrix inversion....

the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...

In this paper, we propose a novel watermarking method that has robust and transparent properties by perceptually tuned characteristics and stationary Generalized Gaussian model based on Multiwavelet transform domain. The proposed method embeds watermark signals at the texture and edge regions using the perceptual stochastic model with content adaptivenes. This method adopts stationary Generaliz...

A pre-processing design using neural networks is proposed for multiwavelet filters. Various numerical experiments are presented and a comparison is given between neural network pre-processing and a preprocessing for solving linear systems. Neural network pre-processing produces a good approximation for a large number of terms and converges repidly. In memoriam Michihiro Nagase To appear in J. o...