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arXiv · 1502.07633

Properties and examples of Faber--Walsh polynomials

Olivier Sète·Jörg Liesen
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Abstract

The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this paper we derive new properties of the Faber--Walsh polynomials, where we focus on results of interest in numerical linear algebra, and on the relation between the Faber--Walsh polynomials and the classical Faber and Chebyshev polynomials. Moreover, we present examples of Faber--Walsh polynomials for two real intervals as well as some non-real sets consisting of several simply connected components.

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Olivier Sète, Jörg Liesen. 2015-02-26. Properties and examples of Faber--Walsh polynomials. https://doi.org/10.1007/s40315-016-0176-9

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