Seminar Details
2015-09-29 (14:00) : Dual minimal bases and their use in the numerical stability of polynomial eigenvalue solvers
At Euler building (A002)
Organized by Mathematical Engineering
Speaker :
Van Dooren, Paul
Abstract :
Joint work with Froilan Dopico (UC3M), Piers Lawrence (UCL) and Javier Perez (UManchester).
In this talk we give a new class of linearizations of a polynomial matrix $P(s) = P_0 + P_1s + \ldots + P_d s^d$ which could be called Fiedler-like linearizations of the polynomial
matrix $P(s)$. The class contains the pencils defined in the work of Fiedler, but also those in the work of Antonio and Vologiannidis. The new characterization of pencils is quite
straightforward and has a block structure that is much easier to describe than the derivations that were given in these earlier papers. Moreover, we show that applying the $QZ$ algorithm
to these pencils results in a backward error that can be mapped back to the coefficients $P_i, i = 0,\ldots, d$, and this in a backward stable manner. Our new approach is heavily based
on the concept of dual minimal polynomial bases, which we also discuss in this talk.