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Solutions to a quadratic inverse eigenvalue problem

✍ Scribed by Yun-Feng Cai; Yuen-Cheng Kuo; Wen-Wei Lin; Shu-Fang Xu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
225 KB
Volume
430
Category
Article
ISSN
0024-3795

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In this paper, we first give the representation of the general solution of the following inverse monic quadratic eigenvalue problem (IMQEP): given matrices Ξ› = diag{Ξ» 1 , . . . , Ξ» p } ∈ C pΓ—p , Ξ» i ΜΈ = Ξ» j for i ΜΈ = j, i, j = 1, . . . , p, X = [x 1 , . . . , x p ] ∈ C nΓ—p , rank(X ) = p, and both Ξ›

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A kind of generalized inverse eigenvalue problem is proposed which includes the additive, multiplicative and classical inverse eigenvalue problems as special cases. Newton's method is applied, and a local convergence analysis is given for both the distinct and the multiple eigenvalue cases. When the