New. Secondary Pe_k Method Of Secondary Epe_k Method

In the networks and controlling fields of engineering, many problems can be described as solving a system of linear algebraic equations Ax - f ,whose matrix of coefficients is large tridiagonal blocked matrix. The usual method of solving this kind of equations is the iterative method. In this paper, a new iterative method will be given. It is to be discussed as follows:(1) The new quadratic PEk method is derived on the base of incompletely LU triangular decomposition. Based on the results, the convergence of the new quadratic PEk method is proved about the Hermite positive definite matrix, M-matrix and H-matrix. In the end, some examples are given to illustrate that the convergence of the new quadratic PEk method is better than PE method and quadratic PE method to proper parameter k.(2) On the results of new quadratic PEk method, the quadratic EPEk method is discussed. The convergence of the quadratic EPEk method is proved in Hermite positive definite matrix. Then the condition of Hermite positive definite matrix is extended to the condition of the positive-definable matrix.