An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG(F )> rX(F ), where rG(F ) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, th...

Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m optimization models are parallelly treat...

We present in this paper several extremely efficient and accurate spectral-Galerkin methods for secondand fourth-order equations in polar and cylindrical geometries. These methods are based on appropriate variational formulations which incorporate naturally the pole condition(s). In particular, the computational complexities of the Chebyshev–Galerkin method in a disk and the Chebyshev–Legendre–...

ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...

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...

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...