In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...

A Chebyshev knot C(a, b, c, φ) is a knot which has a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + φ), where a, b, c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ R. We show that any two-bridge knot is a Chebyshev knot with a = 3 and also with a = 4. For every a, b, c integers (a = 3, 4 and a, b coprime), we describe an algorithm that gives all Cheb...

The major application for watermark is protecting intellectual property rights. In this paper, a watermark scheme with circulation, based on nonoverlapping discrete wavelet transform (DWT) and singular value decomposition (SVD), is presented. First, the original host image and watermark image are divided into nonoverlapping blocks, respectively and to the former DWT and SVD is applied. Second, ...

We studied the informativeness of image features extracted from different lengths of image transform chains for the purpose of image classification. Image features were extracted from the raw images, image transforms, and second, third and fourth order of compound image transforms. The transforms used in this study are Fourier, Chebyshev, and Wavelet (symlet 5) transform. Experimental results s...

Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet r...

16 [16] S. Mallat Multiresolution approximation and wavelet orthonormal bases of L 2 (R) Transactions of AMS. vol 135 (1989) [17] K.J. Marfurt Accuracy of nite-dierence and nite-element modeling of the scalar wave equation. [21] V. Perrier & C. Basdevant La d ecomposition en ondelettes p eriodiques, un outil pour l'analyse de champs inhomog enes. Th eorie et algorithmes. La Recherche A erospati...

We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N . This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This is the first of a series of papers in this area, which solves the longstanding problem of finding a satisfactory mul...

ll rights reserved. Recently the Chebyshev kernel has been proposed for SVM and it has been proven that it is a valid kernel for scalar valued inputs in [11]. However in pattern recognition, many applications require multidimensional vector inputs. Therefore there is a need to extend the previous work onto vector inputs. In [11], although it is not stated explicitly, the authors recommend evalu...

The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...