Abstract
The Seidel method for solving a system of linear algebraic equations and an estimate of the rate of its convergence are considered in this paper. It is proposed to construct an equivalent system for which the Seidel method also converges but yields a better rate of convergence. An equivalent system is constructed by a separate iterative process, where each step requires O(n) operations. The stability of this process is proved. Results of numerical experiments are presented that show an improvement in the estimate of the convergence rate.
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References
D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra (Lan’, St. Petersburg, 2002) [in Russian].
A. N. Borzykh, “Improving an estimate of the convergence rate of the Seidel method by selecting the optimal order of equations in the system of linear algebraic equations,” Comput. Math. Math. Phys. 57, 1–6 (2017). https://doi.org/10.1134/S0965542517010055
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Borzykh, A.N. Improving an Estimate of the Convergence Rate of the Seidel Method. Vestnik St.Petersb. Univ.Math. 52, 127–135 (2019). https://doi.org/10.1134/S1063454119020043
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DOI: https://doi.org/10.1134/S1063454119020043