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 Course on linear systems |
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| 'Solving linear systems with iterative techniques', by Jean-Michel Hervouet
This lecture deals with the numerical solution of large linear systems with sparse matrices, e.g. systems stemming from the finite element method.
A first series of methods are based upon a matrix decomposition leading to the Jacobi method and its variants. Then gradient methods are tackled. After discussing the basics, we gradually move on to the conjugate-gradient method and its allies. Lanczos methods are then treated with the example of GMRES. Eventually all the methods are given with preconditioning, but in a formal way without stating the kind of matrix used for pre-conditioning. All the algorithms of this course are then given in a synthetic way. The link with what is available in the Telemac system is done in the last chapter. |
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