A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington's integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington's integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic ...

This research paper deals with some radius problems, the basic geometricproperties, general coecient and inclusion relations that are established for functionsin a subfamily of analytic functions subordinate to k-Jacobsthal numbers.

In this paper we study the problem of template matching in signals, specifically focusing on images. First we present the solution to the case where the template is translated in the image, then discuss how to locate a template if it appears scaled in the image. The tools used for this scaling algorithm are wavelets, specifically the Haar wavelet. Wavelets naturally encode scaling information, ...

Excessive number of Haar-like features and the complex threshold calculation of covariance matrix feature are two key issues of Adaboost face detection. In this paper, an efficient feature named covariance feature is proposed. The novel method divides the face image into several regions and it calculate covariance feature of any two regions. Then optimal weak classifiers will be picked out by A...

The complicated moments of the traces of unitary and orthogonal Haar distributed random matrices are studied. The exact formulas for different values of moment and matrix orders are obtained.

A wavelet method to the solution for time-fractional partial differential equation, by which combining with Haar wavelet and operational matrix to discretize the given functions efficaciously. The time-fractional partial differential equation is transformed into matrix equation. Then they can be solved in the computer oriented methods. The numerical example shows that the method is effective.

A new method is presented for computation of optimal control for linear systems using Haar wavelets. The method is based on a novel operational matrix derived from integration of Haar wavelets. The optimal control problem is converted to a two-point-boundary-value problem, which is then solved using the Haar wavelet transformation. The proposed method is then extended to the numerical solution ...

In this paper, we propose Speaker Identification using two transforms, namely Haar Transform and Kekre’s Transform. The speech signal spoken by a particular speaker is converted into a spectrogram by using 25% and 50% overlap between consecutive sample vectors. The two transforms are applied on the spectrogram. The row mean of the transformed matrix forms the feature vector, which is used in th...

In this paper, we propose a new modification of rationalized Haar functions called rationalized Haar s-functions for the numerical solution of linear and nonlinear Volterra integral equations of the second kind. By selecting these functions and following the procedure of determining the wavelet expansion coefficients, the calculations are economized. This method converts the integral equation t...

We present a multilevel method for discrete ill-posed problems arising from the discretization of Fredholm integral equations of the first kind. In this method, we use the Haar wavelet transform to define restriction and prolongation operators within a multigrid-type iteration. The choice of the Haar wavelet operator has the advantage of preserving matrix structure, such as Toeplitz, between gr...