New algorithms for matrices, polynomials and matrix polynomials
Amirhossein Amiraslani · 2006
In this thesis, motivated by the problem of finding fast methods to solve systems of polynomial equations when the polynomials are given by their values on a grid, we extend classical methods for the computation of polynomial eigenvalue problems to the Lagrange basis case. We give several new analytic matrix factorings for generalized companion matrices, and discuss their use in Rayleigh Quotient Iteration. We also discuss the use of multivariate division to construct new resultant-like polynomial eigenproblems, and extend a result of Tisseur and Higham [1] on matrix polynomial pseudospectra.