Relaxation Methods for Systems of Linear Equations and Applications
Received:September 30, 2019  Revised:March 17, 2020
Key Word: iterative methods   relaxation methods   linear systems   saddle point problem   PageRank problem  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11871136; 11801382; 11971092) and the Fundamental Research Funds for the Central Universities (Grant No.DUT19LK06).
Author NameAffiliation
Xinzhu ZHAO School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Bo DONG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Bo YU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      The relaxation methods have served as very efficient tools for solving linear system and have many important applications in the field of science and engineering. In this paper, we study an efficient relaxation method based on the well-known Gauss-Seidel iteration method. Theoretical analysis shows our method can converge to the unique solution of the linear system. In addition, our method is applied to solve the saddle point problem and PageRank problem, and the numerical results show our method is more powerful than the existent relaxation methods.
Citation:
DOI:10.3770/j.issn:2095-2651.2020.04.008
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