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