Abstract: This paper studies the fundamental theory of the discrete ill-posed regularization and the generalized minimal residual algorithm (GMRES(m)) based on Krylov subspace methods and specially the relationship between residual vector and Krylov subspace. The techniques are based on the projection process. Discrete ill-posed regularization methods convert ill-posed problems into posed problems, so the generalized minimal residual algorithm can be used in this kind of ill-posed problems. Numerical results show the reliability and efficiency of the algorithm.
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Received: 20 August 2008
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