Properties and examples of Faber--Walsh polynomials
This work provides theoretical insights into a generalization of Faber polynomials, which may benefit numerical linear algebra, but the results are incremental and lack concrete performance numbers.
The paper derives new properties of Faber-Walsh polynomials, focusing on their relevance to numerical linear algebra and their relation to classical Faber and Chebyshev polynomials, and provides examples for two real intervals and non-real sets.
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.