Alternating iterative scheme for the solution of block-structured systems

Šípek, Jan; Zítko, Jan

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Displaying similar documents to “Alternating iterative scheme for the solution of block-structured systems”

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New SOR-like methods for solving the Sylvester equation

Jakub Kierzkowski (2015)

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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.

Using successive approximations for improving the convergence of GMRES method

Jan Zítko (1998)

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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...

Convergence analysis of preconditioned AOR iterative method for linear systems.

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On the choice of subspace for iterative methods for linear discrete ill-posed problems

Daniela Calvetti, Bryan Lewis, Lothar Reichel (2001)

International Journal of Applied Mathematics and Computer Science

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Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.

A one parameter method for the matrix inverse square root

Slobodan Lakić (1997)

Applications of Mathematics

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This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.

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,...