scholarly journals Corrigendum to “Preconditioned iterative method for nonsymmetric saddle point linear systems” [Comput. Math. Appl. 98 (2021) 69–80]

2021 ◽  
Vol 99 ◽  
pp. 1
Author(s):  
Li-Dan Liao ◽  
Guo-Feng Zhang ◽  
Xiang Wang
2014 ◽  
Vol 644-650 ◽  
pp. 1988-1991
Author(s):  
Ting Zhou

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. In this paper, we present preconditioned SSOR iterative method for solving the linear systems. Meanwhile, we apply the preconditioner to H-matrix and obtain the convergence result. Finally, a numerical example is also given to illustrate our results.


2007 ◽  
Vol 49 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Shiliang Wu ◽  
Tingzhu Huang

AbstractBoth Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.


2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Qingbing Liu ◽  
Guoliang Chen

M-(H-)matrices appear in many areas of science and engineering, for example, in the solution of the linear complementarity problem (LCP) in optimization theory and in the solution of large systems for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to convergence for this class of matrices. In this paper, we present some comparison theorems on the preconditioned AOR iterative method for solving the linear system. Comparison results show that the rate of convergence of the preconditioned iterative method is faster than the rate of convergence of the classical iterative method. Meanwhile, we apply the preconditioner toH-matrices and obtain the convergence result. Numerical examples are given to illustrate our results.


2009 ◽  
Vol 87 (5-6) ◽  
pp. 342-354 ◽  
Author(s):  
Vladislav Ganine ◽  
Mathias Legrand ◽  
Hannah Michalska ◽  
Christophe Pierre

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.


2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.


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