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.
Radim Blaheta, P. Byczanski, Roman Kohut (2002)
Applications of Mathematics
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This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits...
Manteuffel, Thomas A., Starke, Gerhard, Varga, Richard S. (1995)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Milan Práger (1993)
Applications of Mathematics
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An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
Tijmen P. Collignon, Martin B. Van Gijzen (2010)
International Journal of Applied Mathematics and Computer Science
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Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods....
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.