Iterative Algorithm For Solving Problem In Matrix Equation And Parameter Estimation Of Controlled Autoregressive

Iterative algorithm as a method to get the matrix solution has been used by many researcher in recent years. The iterative algorithm is very important because we need a high demand for memory if we use the Kronecker product to solve the large matrix. In this paper we consider getting the Hermite solution and bisymmetric hermite solution of the complex matrix equations A1XB1 + C1XD1= M1, A2XB2 +C2XD2 = M2 and the problem of parameter estimation for controlled autoregressive models by the iterative algorithm. The paper is organized as follows:In Chapter One, we introduce some background knowledge and recent works for the iterative algorithm to solve the matrix equations and translate the parameter estimation for controlled autoregressive models to the question of matrix; Then we introduce the basic work of this paper briefly; At last, some related concepts and notations are given in the paper.In Chapter Two, we will get the hermite solution of the matrix equations A1XB1 + C1XD1 = M1,A2XB2 + C2XD2 = M2 by using conjugate gradient algorithms. Then the method will be proved convergence. At last, the simulation example shows that the proposed algorithms work quite well.In Chapter Three, we get the model's parameter by translating the parameter estimation for controlled autoregressive models to the question of matrix. Then we show it is convergent. A numerical example will be given to illustrate the effective-ness of the proposed method at the end.