This paper presents a short survey of convergence results and properties of the Lebesgue function kmn(x) for (0, 1 , . . . , m) Hermite-Fejer interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n -*• oo of the Lebesgue constant Amn = max{Xm n(x) : — 1 < x < 1} for even m is then studied, and new results are obtained for the asymptotic ex...

An interpolation polynomial of order N is constructed from p indepen­ dent subpolynomials of order n '" Nip. Each such subpolynomial is found independently and in parallel. Moreover, evaluation of the polynomial at any given point is done independently and in parallel, except for a final step of summation of p elements. Hence, the algorithm has almost no commu­ ,:.. nication overhead and can be...

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The rst of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis. x1. Introduction Let U denote ...

We study interpolation polynomials based on the points in [−1, 1]× [−1, 1] that are common zeros of quasi-orthogonal Chebyshev polynomials and nodes of near minimal degree cubature formula. With the help of the cubature formula we establish the mean convergence of the interpolation polynomials. 1991 Mathematics Subject Classification: Primary 41A05, 33C50.

A generalized Chebyshev interpolation procedure increasing a fixed number of sample points at a time is developed and analyzed. It is incorporated into an efficient automatic quadrature scheme of Clenshaw-Curtis type. Numerical examples indicate that the present method is efficient not only for well-behaved functions but for those with discontinuous low order derivatives by virtue of adequate e...

ECG (Electrocardiogram) signals originating from heart muscles, generate massive volume of digital data. They need to be compressed or approximated for efficient transmission and storage. ECG signal compression is traditionally performed in three ways: direct, transform and parameter extraction. Polynomial approximation which is a form of parameter extraction method, is employed here. This pape...

It has recently been shown that the Lebesgue constant for Berrut’s rational interpolant at equidistant nodes grows logarithmically in the number of interpolation nodes. In this paper we show that the same holds for a very general class of well-spaced nodes and essentially any distribution of nodes that satisfy a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as ex...

We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications co...