On the Inverse Symmetric Quadratic Eigenvalue Problem
Peter Lancaster, Ion Zaballa · SIAM Journal on Matrix Analysis and Applications · 2014
The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the following form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues. An orthogonality condition dependent on these signs plays a vital role in this construction. Special attention is paid to the cases when the leading and trailing coefficients of the quadratic matrix polynomial are prescribed to be positive definite.