Solutions of the partially described inverse quadratic eigenvalue problem

Yuen Cheng Kuo*, Wen-Wei Lin, Shu Fang Xu

*Corresponding author for this work

Research output: Contribution to journalArticle

34 Scopus citations


Given k pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing nxn real symmetric matrices M, C, and K (with M positive definite) so that the quadratic pencil Q(λ) = λ 2M+λC+K has the given k pairs as eigenpairs. Using various matrix decompositions, we first construct a general solution to this problem with k ≤ n. Then, with appropriate choices of degrees of freedom in the general solution, we construct several particular solutions with additional eigeninformation or special properties. Numerical results illustrating these solutions are also presented.

Original languageEnglish
Pages (from-to)33-53
Number of pages21
JournalSIAM Journal on Matrix Analysis and Applications
Issue number1
StatePublished - 1 Dec 2006


  • Inverse eigenvalue problem
  • Partial eigenstructure assignment
  • Partially prescribed spectrum
  • Quadratic eigenvalue problem

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