On eigenvalues of perturbed quadratic matrix polynomials

Radjabalipour, M.; Salemi, Abbas

doi:10.1007/bf01208352

Cited by 4 publications

(2 citation statements)

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“…Let A(λ) = d i=0 Aiλ i be an n × n matrix polynomial over Q with det A(λ) = 0. Following [20,11,13,12,22,23] we consider the problem of the sensitivity of the eigenvalues of A(λ) (i.e. the roots of det A(λ)) to small perturbations of the matrix coefficients Ai.…”

Section: Introductionmentioning

confidence: 99%

“…Previous studies about parameterized matrix polynomials were concerned by either determinant degree and Smith form computations [17,18,19] or perturbation theory for matrix pencils [7,21], quadratic matrix polynomials [13,22,23] and matrix functions [20,21,11,12]. But the approach that consists in searching for the "best" leading Smith form in a set of equivalent perturbed matrix polynomials seems to be new.…”

Section: Introductionmentioning

confidence: 99%

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A reduced form for perturbed matrix polynomials

Jeannerod

2002

Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation

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We show that every perturbation A(λ,) of an n × n matrix polynomial A(λ) such that det A(λ) = λ m with m ≤ n can be reduced by equivalence transforms to a perturbed matrix polynomial whose leading matrix has maximal Smith form. This yields a reduced form for square perturbed matrix polynomials from which one can easily recover all the eigenvalue leading terms of the form µ β with β −1 ∈ N * .

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