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Combining the preconditioned conjugate gradient method and a matrix iterative method

Jan Zítko (1996)

Applications of Mathematics

The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after m steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.

Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations

Radek Kučera (2005)

Applications of Mathematics

The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results.

Composite grid finite element method: Implementation and iterative solution with inexact subproblems

Radim Blaheta, P. Byczanski, Roman Kohut (2002)

Applications of Mathematics

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 of the described...

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