More on modifications and improvements of classical iterative schemes for M-matrices

Preconditioned Modified Explicit Decoupled Group for the Solution of Steady State Navier-Stokes Equation

“…Assume that the solution at any group of four points on the solution domain is achieved using the rotated equation (10). This will result in a (4x4) system of equations which lead to a decoupled system of (2x2) equations whose explicit forms are given by…”

“…In particular, Ali and Abdullah [4] derived a group explicit method derived from a skewed five-point finite difference approximations where the proposed method was shown to be more efficient in CPU timings than the existing schemes based on the standard five-point difference stencil. With the realization that preconditioning technique is essential for the improvement in the performance of iterative methods, research on preconditioners has moved to center stage in recent years ( [7], [8], [9], [10], [11], [12]). Recently, Ali and Saeed [13] proposed a (I + K)-type preconditioning matrix in block form and applied it to the original system obtained from the four point Explicit Decoupled Group (EDG) method for solving the coupled system of elliptic partial differential Eqs.…”

A Modified Precondition in the Gauss-Seidel Method

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ABSTRACTIn recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). In this paper we use S l instead of (S + S m ) and compare with M. Morimoto's precondition [3] and H. Niki's precondition [5] to obtain better convergence rate.

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Multi-level preconditioned block accelerated overrelaxation iteration method for z-matrices

“…were proposed in [9] and [4] respectively, and further studied in [13]. Similar preconditioners and the comparison theorem were also studied in [2] and [6].…”