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This paper is devoted to the study of perturbations of a matrix pencil,structured or unstructured, such that a perturbed pencil will reproduce a givendeflating pair while maintaining the invariance of the complementary deflatingpair. If the latter is unknown, it is referred to as no spillover updating. Thespecific structures considered in this paper include symmetric, Hermitian,$\star$-even, $\star$-odd and $\star$-skew-Hamiltonian/Hamiltonian pencils.This study is motivated by the well-known Finite Element Model Updating Problemin structural dynamics, where the given deflating pair represents a set ofgiven eigenpairs and the complementary deflating pair represents the remaininglarger set of eigenpairs. Analytical expressions of structure preserving nospillover updating are determined for deflating pairs of structured matrixpencils. Besides, parametric representations of all possible unstructuredperturbations are obtained when the complementary deflating pair of a givenunstructured pencil is known. In addition, parametric expressions are obtainedfor structured updating with certain desirable structures which relate toexisting results on structure preservation of a symmetric positive definite orsemi definite matrix pencil.

Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair