Inverse Problems And The Best Approximation Of Several Symmetrizabble Matrics

A matrix inverse eigenvalue problem concerns the reconstruction of a matrix from prescribed spectral data, and where the spectral data involved may consist of the complete or only partial information of eigenvalues or eigenvectors. This problem has been widely used in structural design, system identification, principal component analysis, electricity, solid mechanics, molecular spectroscopy, structural dynamics, automatics control theory, vibration theory, and so on.The following problems are considered:Where S AB is the set of the solutions of problemâ…¢, i.e.The main achievements of this dissertation are as follows:Let W be a nonsingular matrix.1. Problem I and Problem II are considered under the matrix set S is as the following: 1) the set of real W-symmetrizable matrices; 2) the set of real W-symmetrizable nonnegative definite matrices; 3) the set of real W-symmetrizable matrices on the linear manifold. The sufficient and necessary condition for solving Problem I are given, and the expressions of solutions of Problem I and Problem II are obtained, the related numerical algorithm and some example are provided.2. Problem III and Problem IV are considered under the matrix sets S 1, S 2 is as...