The Weighted Least Squares Solutions Of Several Classes Of Linear Matrix Equations And It's Optimal Approximation Problems

wide range of practical applications, including structure design, parameter identification, biology, automatic control theory, vibration theory, finite elements signal processing and so on.Due to this reason, the study in constrained linear matrix equation has taken good progress, and has become a welcome research topic in computational mathematics.So far, almost all existing research in matrix equation problem focuses on the case where Frobenius norm is used. In this thesis, we define a weighted Frobenius norm A W = WAF. By the use of singular value decomposition and the dual theory in Hilbert space, we study the solution of the following four problems: Problem I: Given Find X such that where SR +m×m denotes m-order real symmetric and positive definite matrix. Problem II: Given . Find X such that Problem III: Given such that where S E denotes the solution set of Problem I or Problem II.The main results of this thesis are listed as follows:1. We derive the expressions of the solution of Problem I and related optimal approximation problem.2. We also derive the expressions of the solution of Problem II and related optimal approximation problem.3. We discuss the least squares symmetric and anti-symmetric solutions of matrix equation BT XB= D on some linear manifold. We also study the related optimal approximation problem.