Preconditioned diagonally dominant property for linear systems with -matrices.
Wang, Xue Zhong, Huang, Ting Zhu, Fu, Ying Ding (2006)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “Convergence analysis of preconditioned AOR iterative method for linear systems.”
Preconditioned diagonally dominant property for linear systems with -matrices.
New SOR-like methods for solving the Sylvester equation
Jakub Kierzkowski (2015)
Open Mathematics
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We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.
Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations
Zahari Zlatev, Krassimir Georgiev (2013)
Open Mathematics
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Many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during the treatment of the original problem, because these systems can be very large (containing up to many millions of equations). It is, therefore,...
Solution of linear algebraic equations with 3-diagonal ill-conditioned system matrix
Pavol Poliak, Mária Postulková, Romana Vyhnanská (1970)
Aplikace matematiky
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Certain methods for the solution of system of linear algebraic equations with ill-conditioned system matrix are compared with the Gaussian method. The considered methods were modified for 3-diagonal systems.
Some results on matrices of class and their application to the convergence rate of iteration procedures
Miroslav Fiedler, Vlastimil Pták (1966)
Czechoslovak Mathematical Journal
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Perron complements of diagonally dominant matrices and H-matrices.
Zeng, Li, Xiao, Ming, Huang, Tin-Zhu (2009)
Applied Mathematics E-Notes [electronic only]
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Using successive approximations for improving the convergence of GMRES method
Jan Zítko (1998)
Applications of Mathematics
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In this paper, our attention is concentrated on the GMRES method for the solution of the system of linear algebraic equations with a nonsymmetric matrix. We perform pre-iterations before starting GMRES and put for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the th powers of eigenvalues of the matrix . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and...