Inverse Eigenvalue Problem Of Matrices

There are all kinds of inverse eigenvalue and generlized inverse eigenvalue problerns in the fields of structural design,vibration system,automation control and matrix decision and so on. Recent years,inverse eigenvalue problem of matrices has become an active topic of computational mathmatics for needs of project and technology.By using of a series of methods in numerical linear algebra,such as the singular value decomposition(SVD) and the generalized singular value decomposition(GSVD),the generalized inverse of a matrix and the linear manifold and so on,thesis has solved problems as follows.1. Solvability Conditions of Inverse Problems for Hermite Generalized Centrosymmetric Positive Semidefinite Matrices.2. Left and Right Inverse Eigenvalue Problem for D-Symmetric Matrices.3. Inverse Problems of D-Symmetric Matrices on The Linear Manifold.Finally, some numerical experiments are given.