Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization

We perform a backward error analysis of polynomial eigenvalue problems solved via linearization. Through the use of dual minimal bases, we unify the construction of strong linearizations for many different polynomial bases. By inspecting the prototypical linearizations for polynomials expressed in a number of classical bases, we are able to identify a small number of driving factors involved in the growth of the backward error. One of the primary factors is found to be the norm of the block vector of coefficients of the polynomial, which is consistent with the current literature. We derive upper bounds for the backward errors for specific linearizations, and these are shown to be reasonable estimates for the computed backward errors.

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