A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate...

In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling lters and wavelet lters) can be factored as the product of primitive parau-nitary matrices, a pseudo identity matrix pair, an invertible matrix, and the canonical Haar matrix. Compared with the f...

A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...

Digital databases can be represented by matrices, where rows (say) correspond to numerical sensors readings, or features, and columns correspond to data points. Recent data analysis methods describe the local geometry of the data points using a weighted affinity graph, whose vertices correspond to data points. We consider two geometries, or graphs one on the rows and one on the columns, such th...

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its...

Abstarct— This paper proposes a digital image watermarking of still images using self-kronecker product of orthogonal transforms and Singular Value Decomposition. Singular Value Decomposition is used due to its high stability and high image energy compaction in few numbers of singular values. Kronecker product of two transforms helps us to focus on only global features and not the local feature...

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

Texture is the term used to characterize the surface of a given object or phenomenon and is an important feature used in image processing and pattern recognition. Our aim is to compare various Texture analyzing methods and compare the results based on time complexity and accuracy of classification. The project describes texture classification using Wavelet Transform and Co occurrence Matrix. Co...

Let M be an n × n matrix with i.i.d. CN(0, 1) entries (Complex Normal random variables with mean 0 and variance 1), and define A = M +M ∗ √ 2 , where M∗ denotes the conjugate transpose of M . The resulting random matrix is a member of the Gaussian Unitary Ensemble (GUE), and we would like to classify the distribution of its eigenvalues. In a previous section, the measure of the Gaussian Unitary...

This paper presents a computational method for solving stochastic ItoVolterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error...