The Application Of Pretreatment Technology In The Constrained Matrix Equation Iterative Method

The constrained matrix equation problem is to find solution of a matrix equation in aconstrained matrix set. Different constrained conditions or different matrix equations lead todifferent constrained matrix equation problem. The constrained matrix equation problem hasbeen one of the hottest topics in the filed of numerical algebra in rencent years, and it appliedin many fields, such as structure design, molecule spectroscopy, oscillation theory, linearprogramming and non-linear programming theory, optics and finite element theory etc.The main works as follows:1. The polynomial pretreatment method for the Hermite and the anti-Hermite solution ofthe matrix equation AX = Bis considered. Firstly, by making use of the ideas of pretreatmentpolynomial; and the polynomial pretreatment orthogonal projection iteration method is putforward by combining the polynomial pretreatment matrix C ( A|- ); then the estimation ofconvergence rate is obtained. Also, the numerical experiments are provided to indicate theeffectiveness and feasibility of this method.2. The polynomial pretreatment method for the Hermite and the anti-Hermite solution ofthe matrix equation A~HXA= Bis considered. For initial matrix, the solution of theconstrained matrix equation can be determined within finite iteration steps in the absence ofround-off errors. By making use of the pretreatment method properly, the numericalexperiments indicate that the convergence rate of algorithm will be improved significantly.3. In Chapter 4, the polynomial pretreatment method of the inverse eigenvalue problemAX = XΛis considered. Analogous with the above method, the polynomial pretreatmentmatrix C ( X|- )is deprived. Furthermore, corresponding polynomial pretreatment orthogonalprojection iteration algorithm is included. The estimation of convergence rate can also bedeprived, and then the results of numerical experiments are given that support the claim.