Abstract: The inverse problem of quadratic eigenvalue is an inverse process of quadratic eigenvalue problem, and it is widely used in the field of structural dynamic model correction. Given part of eigenvalues and eigenvectors, based on the singular value decomposition of matrix, block matrix method and generalized inverse of Moore-Penrose, the inverse quadratic eigenvalue problem of constructing anti-reflexive matrices is considered in this paper. Then, a general expression of solution to the problem is presented. Moreover, the existence and uniqueness of the optimal approximation problem associated with solution set is discussed. Finally, the expression and numerical method are proposed, the correctness of the result is verified by a numerical example.

Key words: anti-reflexive matrix, quadratic eigenvalue problem, singular value decomposition, optimal approximation solution