Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Title

Numerical Results on the Zeros of Faber Polynomials for m-fold Symmetric Domains

Event Name/Location

American Mathematical Society Summer Seminar in Applied Mathematics / Colorado State University, Ft. Collins, CO

Document Type

Conference Proceeding

Publication Date

1992

Abstract

Faber polynomials, generated by a conformal mapping Φ(z) of the exterior of a set E onto the exterior of a circle, have well-known classical applications in numerical analysis as basis sets for polynomial and rational approximations in the complex plane. The structure of the Faber polynomials of a given set E is essential for such applications. In this paper we study the Faber polynomials associated with m-fold symmetric domains. A new determinant representation which relates the zeros of Faber polynomials to the eigenvalues of a certain matrix is derived and numerical computations on the zeros of Faber polynomials associated with symmetric lunes and m-gons are illustrated.

Conference Proceeding Title

Lectures in Applied Mathematics: Volume 29: Exploiting Symmetry in Applied and Numerical Analysis

ISBN

978-0-8218-1134-4

Publisher

American Mathematical Society

First Page

229

Last Page

240