We propose a restarted Arnoldi’s method with Faber polynomials and discuss its use for computing the rightmost eigenvalues of large non hermitian matrices. We illustrate, with the help of some practical test problems, the benefit obtained from the Faber acceleration by comparing this method with the Chebyshev based acceleration. A comparison with the implicitly restarted Arnoldi method is also ...

For a compact set E ⊂ C containing more than two points, we study asymptotic behavior of normalized zero counting measures {μk} of the derivatives of Faber polynomials associated with E. For example if E has empty interior, we prove that {μk} converges in the weakstar topology to a measure whose support is the boundary of g(D), where g : {|z| > r} ∪ {∞} → C\E is a universal covering map such th...

The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

This paper is to complete and improve the work reported in 1, 2], using the Lanczos-method (in Coleman's version) to approximate the Bessel functions Y 0 (z) and Y 1 (z). We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the-method. Numerical comparison among the pow...