Discrete differential operators in multidimensional Haar wavelet spaces

Discrete differential operators in multidimensional Haar wavelet spaces

We consider a class of discrete differential operators acting on multidimensional Haar wavelet basis with the aim of finding wavelet approximate solutions of partial differential problems. Although these operators depend on the interpolating method used for the Haar wavelets regularization and the scale dimension space, they can be easily used to define the space of approximate wavelet solution...

Optimal quadrature for Haar wavelet spaces

This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, Hwav . The asymptotic orders of the errors are derived for the case of the scrambled (λ, t,m, s)-nets and (t, s)-sequences. These rules are shown to have the b...

On topology in multidimensional discrete spaces

The Segmented-Matrix Algorithm for Haar Discrete Wavelet Transform

Discrete wavelet transform (DWT) is an efficient tool for multi-resolution decomposition of images. It has been shown to be very promising due to its high compression ratio and self-similar data structure. Conventionally a 2-D DWT is accomplished by performing two 1-D operations: one along the rows and the other along the columns of an image. Without executing ordered 1-D transforms, we develop...

A Novel Decision Tree Framework using Discrete Haar Wavelet Transform

Data Mining is a popular knowledge discovery technique. In data mining decision trees are of the simple and powerful decision making models. One of the limitations in decision trees is towards the data source which they tackle. If data sources which are given as input to decision tree are of imbalance nature then the efficiency of decision tree drops drastically, we propose a decision tree stru...