Displaying similar documents to “On an accelerated procedure of extrapolation.”

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.

Convergence of the accelerated overrelaxation method

Dragoslav Herceg, Ljiljana Cvetković (1989)

Aplikace matematiky

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The convergence of the Accelerated Overrelaxation (AOR) method is discussed. It is shown that the intervals of convergence for the parameters σ and ω are not always of the following form: 0 ≤ ω ≤ ω 1 , - σ 1 ≤ σ ≤ σ 2 , σ 1 , σ 2 ≥ 0 .

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 ( I - T ) x = b of linear algebraic equations with a nonsymmetric matrix. We perform m pre-iterations y l + 1 = T y l + b before starting GMRES and put y m for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the m th powers of eigenvalues of the matrix T . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and...