Title: Polynomial eigenvalue bounds obtained from generalizations of scalar polynomial properties
Speaker: Professor Aaron Melman, Santa Clara University
Date: November 30, 2017
Location: Y2E2 111
We consider localization results for the zeros of scalar polynomials
that do not appear to be widely known, and generalize them to matrix
polynomials to construct bounds on polynomial eigenvalues. Such
bounds are useful, e.g., for iterative methods when computing
pseudospectra, or especially in the analysis of engineering problems.
Polynomial eigenvalues are much more difficult to compute than
polynomial zeros, making bounds on them more valuable. Contrary to
most existing results, our eigenvalue localization regions can be
iteratively improved. We also obtain results for generalized
polynomial bases that include, but are not limited to, all classical
orthogonal bases: Hermite, Legendre, Chebyshev, etc. We present
several applications from the engineering literature.