Perturbation theory of structured matrix pencils with no spillover

This paper aims to determine unstructured or structured perturbations of a matrix pencil such that the perturbed matrix pencil reconstructs a given deflating pair without changing the complementary deflating pair of the unperturbed matrix pencil. If the latter is unknown, then it is referred to as no spillover updating. If the complementary deflating pair of the given pencil is known, then all possible unstructured perturbations are obtained. However, if the complementary deflating pair of the unperturbed pencil is unknown, then we obtain a class of structure-preserving perturbations of the structured pencil. Finally, these results are utilized to obtain parametric solutions of the model updating problem with no spillover for various structured matrix pencils.& COPY; 2023 Elsevier Inc. All rights reserved.