Adaptive bivariate Chebyshev approximation

Bivariate Lagrange Interpolation at the Chebyshev Nodes

We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all poly...

Discrete linear Chebyshev approximation

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Generalized Rational Chebyshev Approximation

In this paper, a generalized rational Chebyshev approximation problem is considered. The problem is this: To minimize the maximum absolute value of the "criterion function" of the error. By imposing a rather natural restriction on the criterion function, the problem is solved completely; the existence, the uniqueness and the characterization of the best approximation are clarified and interesti...

On Reverse Chebyshev Approximation

We investigate the problem of determining the largest domain where given error bounds can be satissed by an approximation of a given continuous real valued real function using polynomials of several kinds. Since the the error bounds are xed and the domain is variable we call this problem reverse Chebyshev approximation.

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules