Secondary Pe Method

In the networks and controlling fields of engineering, many problenis can be described as solving a system of linear algebraic equationsAX=fWhose matrix of coefficients is large tridiagonal blocked matrix The usual method of solving this kind of equations is the iterative method Iii this paper, a new iterative method will be given. It is to be discussec as follows:(1)The quadratic PE method is derived on the base of incompletely LU triangular decomposition. Based on the results, the convergence of the quadratic PE method in positive definite matrix and diagomdlv dominant L matrix is proved, and the availability of the method is ~iIso illustrated .ln the end, some examples are given to illustrate the method(2)On the results of quadratic PE method, the parameter k is introduced and the convergence of the quadratic PE method is impro\ ed. The convergence of the quadratic PE k method is proved about the Hermite matrix, M-matrix and H-matrix. In chapter four, some examples are given to illustrate that the convergence of quadratic PEk method is better than the quadratic PE method to proper parameter k.