ABSTRACT: In numerical linear algebra, an iterative method that alternates between applying a matrix and taking linear combinations of the result corresponds to applying a polynomial to a matrix. The action of the polynomial on the eigenvalues of the matrix determines the output of the method. In this talk, we'll present a class of polynomial families based on mean-zero random walks which are closely related to Faber polynomials, with useful boundedness and rapid-growth properties on the complex plane. Additionally, we'll present a momentum-based acceleration scheme for the power iteration that significantly outperforms the power iteration for certain classes of non-symmetric matrices with small spectral gaps.

This talk is based on joint work with Nicholas Marshall and Sara Pollock.