The Proconditioning Iterative Methods For The Solution Of The Linear System With Special Coefficient Matric

It's an interested object in Numerical Anlysis to find the solution of linear algebraic equations, which in particular, comes from elliptic partial differential equations. For general linear algebraic equations with huge data, the classical iterative methods (Jacobi and Gauss-Seidel etc) are not always valid, or even if it is convergent, it may convergege very slow. Hence People try to devalop or modify the skill of classical iterative method for some particular coefficient matrices, such as, for Z-matrices and Q-matrices. The preconditioning iterative method is one of most useful treatment.In this paper, we discussed the blocked matrices with Property A or the index p cycle matrices, the main results are:(1) When the coefficient matrice is with Property A , we educe the relation between preconditionging Jacobi , GS, SGS iterative matrices' and classical iterative matrices' eigenvalue; As an application, when take some preconditioning iterative factor, the preconditioning iterative methods may converge quickly even if classical Jacobi iterative is divergent.(2) When the coefficient matrice is index p cycle matrice (p = 3,4,5),we educe the relation between preconditionging Jacobi , GS iterative matrices' and classical Jacobi iterative matrices' eigenvalue; As an application, make some preconditioning iterative factors, when classical Jacobi iterative converge, the preconditioning iterative methods may converge faster.(3) Make an example of matrices with Property A, indicated the precondition iterative's superiority.