New algorithms for matrices, polynomials and matrix polynomials

Authors:
Amirhossein Amiraslani
Affiliations:
The University of Western Ontario (Canada)
Venue:
New algorithms for matrices, polynomials and matrix polynomials
Year:
2006

Citing 0
Cited 6

Computing the topology of a real algebraic plane curve whose equation is not directly available

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Block LU factors of generalized companion matrix pencils

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Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis

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Using implicit equations of parametric curves and surfaces without computing them: Polynomial algebra by values

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Pseudospectra of exponential matrix polynomials

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Abstract

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.