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Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials
Jared Aurentz, Thomas Mach, Leonardo Robol +2
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigen…
Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil
Jared L. Aurentz, Thomas Mach, Leonardo Robol +2
This work is a continuation of "Fast and backward stable computation of roots of polynomials" by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analy…
A framework for structured linearizations of matrix polynomials in various bases
Leonardo Robol, Raf Vandebril, Paul Van Dooren
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described b…