Volume 16, Issue 2
Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations

D. K. Salkuyeh

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 164-170

Published online: 2007-05

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  • Abstract
The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as preconditioners for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.
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@Article{NM-16-164, author = {D. K. Salkuyeh}, title = {Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {2}, pages = {164--170}, abstract = { The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as preconditioners for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10074.html} }
TY - JOUR T1 - Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations AU - D. K. Salkuyeh JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 164 EP - 170 PY - 2007 DA - 2007/05 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/10074.html KW - AB - The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as preconditioners for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.
D. K. Salkuyeh. (2007). Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations. Numerical Mathematics, a Journal of Chinese Universities. 16 (2). 164-170. doi:
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