Hierarchical Identification Principle and a Family of Iterative Methods

In this paper, we extend the well-known Jacobi and Gauss-Seidel iterations to present a large family of iterative methods. The proposed methods are applied to develop iterative solutions to the matrix equation AXB = F and the generalized Sylvester matrix equation AXB + CXD = F by means of a hierarchical identification principle. We prove that the iterative solutions converge to the exact solutions for any initial values. The algorithms proposed require less storage capacity than the existing numerical ones. The iterative methods can be applied to system parameter identification problems.