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MATHEMATICAL MODELING AND NUMERICAL SIMULATION
Two families of the simple iteration method, in comparison
P. N. Sorokina, N. N. Chentsovab a Scientific-Research Institute for System Studies, Russian Academy of Sciences (NIISI RAN), Nakhimovskii av. 36-1, Moscow, 117218, Russia
b Moscow State University, Faculty of Mechanics and Mathematics, MSU, Glavnoe Zdanie, GSP-1, Leninskiye Gory, Moscow, 119991, Russia
Abstract:
Convergence to the solution of the linear system with real quadrate non singular matrix A with real
necessary different sign eigen values of two families of simple iteration method: two-parametric and symmetrized
one-parametric generated by these A and b is considered. Also these methods are compared when matrix
A is a symmetric one. In this case it is proved that the coefficient of the optimal compression of two-parametric
family is strongly less than the coefficient of the optimal compression of symmetrized one-parametric family of
the simple iteration method.
Keywords:
simple iteration method, symmetric matrix.
Received: 26.05.2011 Revised: 21.02.2012
Citation:
P. N. Sorokin, N. N. Chentsova, “Two families of the simple iteration method, in comparison”, Computer Research and Modeling, 4:1 (2012), 5–29
Linking options:
https://www.mathnet.ru/eng/crm465 https://www.mathnet.ru/eng/crm/v4/i1/p5
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Abstract page: | 145 | Full-text PDF : | 72 | References: | 33 |
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