In this poster, we briefly present some results on eigenvalue backward errors of matrix pencils and polynomials under structure preserving perturbations. We also present eigenvalue backward errors of real matrix pencils with respect to real perturbations that also preserve certain structures like symmetric, T-alternating and T-palindromic. Numerical results show that there is a significant difference between the backward errors with respect to perturbations that preserve structures and those with respect to arbitrary perturbations.
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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory