Backward Error of Matrix Rational Function

05/25/2021

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by   Namita Behera, et al.

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We consider a minimal realization of a rational matrix functions. We perturb the polynomial part and one of the constant matrices from the realization part. We derive explicit computable expressions of backward errors of approximate eigenvalue of rational matrix function. We also determine minimal perturbations for which approximate eigenvalue are exact eigenvalue of the perturbed matrix rational functions.