The Least Squares Solutions of Bisymmetric Matrix for Inverse Quadratic Eigenvalue Problem

Abstract

The inverse eigenvalue problem of constructing bisymmetric matrices M , C and K of size n for the quadratic pencil so that has a prescribed subset of eigenvalues and eigenvectors is discussed. A general expression of solution to the problem is provided. The set of such solutions is denoted by S . The optimal approximation problem associated with is posed, that is: to find