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...

Efficient direct solvers based on the Chebyshev-Galerkin methods for second and fourth order equations are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with special structured matrices which can be efficiently inverted. Numerical results indicate that the direct solvers presented in this paper are significantly more accurate...

In this paper we propose the use of a technique based on Chebyshev polynomials approximation for determining the minimum-time rest-to-rest openloop control law for multi-input multi-output (MIMO) continuous-time systems with input and output constraints. The optimal input can be determined, without discretising the system, by suitably approximating the state variables and the input signals by m...

In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation the same as the spectral method so that there is no new mathematical principle involved. We show by numerical examples that the new approach works well and there is indeed no sign...

This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, e...

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...

We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.

Orthogonal Frequency Division Multiplexing (OFDM) systems have been widely used as a communication system. In OFDM systems, there are two main problems. One of them is that OFDM signals have high Peak-to-Average Power Ratio (PAPR). The other problem is that OFDM signals have large side-lobes. In particular, to reduce side-lobes, UniversalFiltered OFDM (UF-OFDM) systems have been proposed. In th...

Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to behavior Lagrange interpolation polynomials continuous absolute value function. Our study establishes error polynomial interpolants function |x| on [−1,1], using Chebyshev and Chebyshev–Lobatto nodal systems with an even number points. Moreover, respect odd cases, relevant change...