Volume 26, pp. 439-452, 2007.

Electrostatics and ghost poles in near best fixed pole rational interpolation

Joris Van Deun

Abstract

We consider points that are near best for rational interpolation with prescribed poles in the same sense that Chebyshev points are near best for polynomial interpolation. It is shown that these interpolation points satisfy an electrostatic equilibrium problem involving the fixed poles and certain ‘ghost’ poles. This problem is closely related to Lamé equations with residues of mixed sign.

Full Text (PDF) [206 KB]

Key words

Rational interpolation, Chebyshev weight, zeros, potential theory.

AMS subject classifications

Primary 33C45, secondary 42C05.

Links to the cited ETNA articles

[7]Vol. 19 (2005), pp. 37-47 A. Garrido, J. Arvesú, and F. Marcellán: An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials

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