Abstract:In this paper, we derive backward error formulas of two approximate eigenpairs of a semisimple eigenvalue with multiplicity two for structured and unstructured matrix pencils. We also construct the minimal structured perturbations with respect to the Frobenius norm such that these approximate eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil. The structures we consider include T-symmetric/T-skewsymmetric, Hermitian/skew-Hermitian, T-even/T-odd, and H-even/H-odd matrix pencils. Furt… Show more
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