It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundstrom theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resul...

Interpolation polynomial pn at the Chebyshev nodes cosπj/n (0 ≤ j ≤ n) for smooth functions is known to converge fast as n → ∞. The sequence {pn} is constructed recursively and efficiently in O(n log2 n) flops for each pn by using the FFT, where n is increased geometrically, n = 2i (i = 2, 3, . . . ), until an estimated error is within a given tolerance of ε. This sequence {2j}, however, grows ...

An algorithm for a generalized Chebyshev interpolation procedure, increasing the number of sample points more moderately than doubling, is presented. The FFT for a real sequence is incorporated into the algorithm to enhance its efficiency. Numerical comparison with other existing algorithms is given.

This correspondence presents a new method for discrete representation of signals { g ( t ) , IE [ O , L ] , g e C*(O, L ) } consisting of a cascade having two stages: a) nonuniform sampling according to Chebyshev polynomial roots; and b) discrete cosine transform applied on the nonuniformly taken samples. We have proved that the considered signal samples and the coefficients of the correspondin...

In this paper, we give a unified approach to error estimates for interpolation on sparse Gauß–Chebyshev grids for multivariate functions from Besov–type spaces with dominating mixed smoothness properties. The error bounds obtained for this method are almost optimal for the considered scale of function spaces. 1991 Mathematics Subject Classification: 41A05, 41A63, 65D05, 46E35

This paper considers a problem of Chebyshev approximation by interpolating rationals. Examples are given which show that best approximations may not exist. Sufficient conditions for existence are established, some of which can easily be checked in practice. Illustrative examples are also presented.

In the present paper polynomial interpolating scaling function and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function efficient algorithms based on fast discrete cosine and sine transforms are proposed.