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On a class of inverse quadratic eigenvalue problem

✍ Scribed by Yongxin Yuan; Hua Dai

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 241 KB
Volume: 235
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2010.11.017

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✦ Synopsis

In this paper, we first give the representation of the general solution of the following inverse monic quadratic eigenvalue problem (IMQEP): given matrices Λ = diag{λ 1 , . . . , λ p } ∈ C p×p , λ i ̸ = λ j for i ̸ = j, i, j = 1, . . . , p, X = [x 1 , . . . , x p ] ∈ C n×p , rank(X ) = p, and both Λ and X are closed under complex conjugation in the sense that λ 2j = λ2j-1 ∈ C,

Frobenius norm and S DK is the solution set of IMQEP. We show that the best approximation solution ( D, K ) is unique and derive an explicit formula for it.

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