Iterative Methods for Linear Systems - Theory and Applications
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چکیده
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منابع مشابه
On 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 کاملComparison 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 کاملA New Two-stage Iterative Method for Linear Systems and Its Application in Solving Poisson's Equation
In the current study we investigate the two-stage iterative method for solving linear systems. Our new results shows which splitting generates convergence fast in iterative methods. Finally, we solve the Poisson-Block tridiagonal matrix from Poisson's equation which arises in mechanical engineering and theoretical physics. Numerical computations are presented based on a particular linear system...
متن کاملFinite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...
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.
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تاریخ انتشار 2014