Numerical Results on the Zeros of Faber Polynomials for m-fold Symmetric Domains
American Mathematical Society Summer Seminar in Applied Mathematics / Colorado State University, Ft. Collins, CO
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
American Mathematical Society
He, Matthew, "Numerical Results on the Zeros of Faber Polynomials for m-fold Symmetric Domains" (1992). Mathematics Faculty Proceedings, Presentations, Speeches, Lectures. 357.