‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

This paper first shows that the Cohen-Daubechies-Feauveau (C-D-F) biorthogonal wavelet can be derived from the interpolating wavelet through a lifting process. Its high-pass filter measures the interpolation error of the averaged data. Next, we propose a new wavelet method, called the difference wavelet method, for efficient representation for functions on R. Its analysis part is simply averagi...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

In this paper, the use of nonseparable wavelets for tomographic reconstruction is investigated. Local tomography is also presented. The algorithm computes both the quincunx approximation and detail coefficients of a function from its projections. Simulation results showed that nonseparable wavelets provide a reconstruction improvement versus separable wavelets.

Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of M = ( 1 1 1 −1 )-wavelets is obtained.

The fundamental ideas of wavelets are introduced within the context of mathematical physics. We present essential background notions of mathematical bases, and discuss Fourier, polynomial, and wavelets bases in this light. We construct several types of wavelets and wavelet-like bases and illustrate their use in algorithms for the solution of a variety of integral and di erential equations.

We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.

In this paper, we give an algorithm to construct semi-orthogonal symmetric and anti-symmetric M-band wavelets. As an application, some semi-orthogonal symmetric and anti-symmetric M-band spline wavelets are constructed explicitly. Also we show that if we want to construct symmetric or anti-symmetric M-band wavelets from a multiresolution, then that multiresolution has a symmetric scaling function.

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...