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.

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parametrization of wavelet space, one can deene a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus g to the (g ? 1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorizatio...

In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting measures using limits of spherical integrals obtained in [46,47]. As examples, obtain 1. empirical distribution diagonal entries $UB_NU^*$, sequence $N\times N$ matrices $B_N$ unitary Haar distributed $U$; 2. upper bound eigenvalue $A_N+UB_NU^*$, two sequence...

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 ...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

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...

Orthonormal systems in commutative L2 spaces can be used to classify Banach spaces. When the system is complete and satisfies certain norm condition the unconditionality with respect to the system characterizes Hilbert spaces. As a noncommutative analogue we introduce the notion of unconditionality of operator spaces with respect to orthonormal systems in noncommutative L2 spaces and show that ...

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...

This informal set of notes contains some of the new results which will appear in the author’s 2013 dissertation. We show that every infinite product of locally compact non-compact groups decomposes into the disjoint union of a Haar null set and a meager set, which gives a partial positive answer to a question of Darji. We also show that the compact sets in each such product group are always Haa...