Study of Numerical Solution of Linear System of Equations by Using SOR Algorithm with \(0<\omega<2\)
DOI:
https://doi.org/10.26713/cma.v12i4.1766Keywords:
Jacobi method, Gauss-Seidal method, Richardson method, SOR method, Spectral radiusAbstract
In this paper, we are studying new approaches in numerical accuracy of the linear system of equations by successive over-relaxation method, analyzing the convergence criteria of iterative methods and comparing the SOR method with other iterative methods. We have shown SOR method converges more rapidly with the others with the help of some typical examples. All the calculations have been performed with the help of MATLAB 2020R.
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F. Curtis, G. Patrick and O. Wheatley, Applied Numerical Analysis, 5th edition, Addison-Wesley, New York (1998), URL: http://www.cse.iitm.ac.in/~vplab/downloads/opt/Applied%20Numerical%20Analysis.pdf.
T. K. Enyew, G. Awgichew, E. Haile and G. D. Abie, Second-refinement of Gauss-Seidel iterative method for solving linear system of equations, Ethiopian Journal of Science and Technology 13(1) (2020), 1 – 15, DOI: 10.4314/ejst.v13i1.1.
W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, Heidelberg — New York (1994), DOI: 10.1007/978-1-4612-4288-8.
L. A. Hageman and D. M. Young, Applied Iterative Methods, Academic Press, New York (1981), URL: https://www.math.hkust.edu.hk/~mamu/courses/531/Applied_Iterative_Methods.pdf.
W. Kahan, Gauss-Seidel Methods for Solving Large Systems of Linear Equations, Ph.D. Thesis, University of Toronto, Toronto, Ontario, Canada (1958).
S. Karunanithi, N. Gajalakshmi, M. Malarvizhi and M. Saileshwari, A study on comparison of Jacobi, Gauss-Seidel and SOR methods for the solution in system of linear equations, International Journal of Mathematics Trends and Technology 56(4) (2018), 214 – 222, DOI: 10.14445/22315373/IJMTT-V56P531.
M. Louka, Iterative Methods for the Numerical Solution of Linear Systems, PhD Thesis, Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece, URL: https://www.di.uoa.gr/sites/default/files/documents/grad/phdbook/Louka.pdf.
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM – Society for Industrial and Applied Mathematics (2003), DOI: 10.1137/1.9780898718003.
J. Xu, A new class of iterative methods for nonselfadjoint or indefinite problems, SIAM Journal on Numerical Analysis 29(2) (1992), 303 – 319, DOI: 10.1137/0729020.
D. M. Young, Iterative Solution of Large Linear Systems, Dover Publications (1971), URL: http://gen.lib.rus.ec/book/index.php?md5=1b9a661e5563daba113b7ffc30d26c18.
D. M. Young, Iterative methods for solving large systems of linear equations, Acta Universitatis Carolinae. Mathematica et Physica 15(1-2) (1974), 179 – 188, URL: http://dml.cz/dmlcz/142353.
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