Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

This paper presents a general approach to a multiresolution analysis and wavelet spaces on the interval Our method is based on the Chebyshev transform correspond ing shifts and the discrete cosine transform DCT For the wavelet analysis of given functions e cient decomposition and reconstruction algorithms are proposed using fast DCT algorithms As examples for scaling functions and wavelets poly...

In this paper, we will introduce a method to find a numerical solution of nonlinear age-structured population model using second-kind Chebyshev polynomials. This method convert the nonlinear age-structured population models to an equivalent differential equation. We introduce two variable second-kind Chebyshev polynomials and their basic properties. These properties will be used to reduce the o...

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...

We present a new kind of second generation wavelets on a rectangular grid. These wavelets are constructed using a 2D lifting scheme which is based on a red-black blocking scheme. Compared to classical tensor product wavelets on the same grid, these new wavelets show less anisotropy. The performance of the new wavelets is compared to tensor product wavelets in an image denoising application.

Analytical solutions of integral equations, either do not exist or are hard to find. Due to this, many numerical methods have been developed for finding the solutions of integral equations. The use of wavelets has come to prominence during the last two decades. Wavelets can be used as analytical tools for signal processing, numerical analysis and mathematical modeling. The early works concernin...