The recently proposed Chebyshev-like lifting map for the zeros of a uni-variate polynomial was motivated by its applications to splitting a univariate polynomial p(x) numerically into factors, which is a major step of some most eeective algorithms for approximating polynomial zeros. We complement the Chebyshev-like lifting process by a descending process, decrease the estimated computational co...

A limited diffraction beams ~LDB! imaging system with Chebyshev weighting is presented. The objective of the paper is to reduce the sidelobes of the LDB without impacting on main-lobe performance and increase the contrast-resolution of the imaging system. The Chebyshev weighting is applied to the LDB and an analytic description and the simulation results are obtained. Theoretical analysis and s...

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...

Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...

We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R2 containing the origin is a zonoid, i.e., the range of a two dimensional vector measure, and we prove that a two dimensional zonoid whose boundary contains the origin is strictly convex if and only if it is the range of a Chebyshev measure. We give a condition under which a two dimension...

We analyze the Legendre and Chebyshev spectral Galerkin semidiscretizations of a one dimensional homogeneous parabolic problem with nonconstant coefficients. We present error estimates for both smooth and nonsmooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we find an arbitrary high order of convegence.

Through a geometncal approach of the blossoming pnnciple, we achieve a dimension élévation process for extended Chebyshev spaces Applied to a nested séquence ofsuch spaces included in a polynomial one, this allows to compute the Bézier points from the initial Chebyshev-Bézier points This method leads to interesting shape effects © Elsevier, Paris

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

This paper is concerned with the problem of nonlinear simultaneous Chebyshev approximation in a real continuous function space. Some results on existence are established, in addition to characterization conditions of Kolmogorov type and also of alternation type. Applications are given to approximation by rational functions, by exponential sums and by Chebyshev splines with free knots.  2003 El...

This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...