### Abstract

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
^{2}M+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 language | English |
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Pages (from-to) | 33-53 |

Number of pages | 21 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 29 |

Issue number | 1 |

DOIs | |

State | Published - 1 Dec 2006 |

### Keywords

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

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## Cite this

*SIAM Journal on Matrix Analysis and Applications*,

*29*(1), 33-53. https://doi.org/10.1137/05064134X