Research On Iterative Algorithm For Sylvester Matrix Equations

Sylvester matrix equations play an important role in many fields,such as signal processing,neural network,model reduction and image restoration etc.It is difficult to achieve exact solutions.Meanwhile,numerical solutions are important in various fields.Hence,it is significantly important to develop efficient algorithms to gain numerical solutions since they can be applied in so many areas.Recently,the algorithm for the solution of matrix equations has attracted many researchers.This paper is concerned with iterative solutions to di-verse Sylvester matrix equations.By applying the hierarchical identification principle,the equation is decomposed into two subsystems.Then by introducing a relaxation parameter,an iterative algorithm is constructed to solve generalized Sylvester matrix equations AXB + CXD = F.Convergence analysis shows that the iterative solutions converge to the exact solutions for any initial values under certain assumptions.Then this paper presents a gradient based iterative algorithm for extended Sylvester matrix equations with a p unique solution?A_iXB_i=C.Then Real domain is extended to complex field.For a class of i=1 equations AXB + CXD = F and the extended Sylvester-conjugate matrix equations m n?A_jXB_j+?C_iXD_i = F,iterative algorithms are constructed.By applying a real j=1 i=1 representation of a complex matrix as a tool and using some properties of the real representation,convergence analysis indicates that the iterative algorithms have stability and accuracy.Finally,numerical examples are given to illustrate the efficiency of the proposed approachs.