Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices
نویسندگان
چکیده
In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results. Keywords—Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.
منابع مشابه
Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems
Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...
متن کاملOn the modified iterative methods for $M$-matrix linear systems
This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...
متن کاملImprovements of two preconditioned AOR iterative methods for Z-matrices
In this paper, we propose two preconditioned AOR iterative methods to solve systems of linear equations whose coefficient matrices are Z-matrix. These methods can be considered as improvements of two previously presented ones in the literature. Finally some numerical experiments are given to show the effectiveness of the proposed preconditioners.
متن کاملSome Results on New Preconditioned Generalized Mixed-Type Splitting Iterative Methods
In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally...
متن کاملOn the modification of the preconditioned AOR iterative method for linear system
In this paper, we will present a modification of the preconditioned AOR-type method for solving the linear system. A theorem is given to show the convergence rate of modification of the preconditioned AOR methods that can be enlarged than the convergence AOR method.
متن کامل