On IGMRES: An incomplete generalized minimal residual method for large unsymmetric linear systems |
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Authors: | Zhongxiao Jia |
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Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, 116024 Dalian, China |
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Abstract: | The truncated version of the generalized minimal residual method (GMRES), the incomplete generalized minimal residual method
(IGMRES), is studied. It is based on an incomplete orthogonalization of the Krylov vectors in question, and gives an approximate
or quasi-minimum residual solution over the Krylov subspace. A convergence analysis of this method is given, showing that
in the non-restarted version IGMRES can behave like GMRES once the basis vectors of Krylov subspace generated by the incomplete
orthogonalization are strongly linearly independent. Meanwhile, some relationships between the residual norms for IOM and
IGMRES are established. Numerical experiments are reported to show convergence behavior of IGMRES and of its restarted version
IGMRES(m).
Project supported by the China State Key Basic Researches, the National Natural Science Foundation of China (Grant No. 19571014),
the Doctoral Program (97014113), the Foundation of Returning Scholars of China and the Natural Science Foundation of Liaoning
Province. |
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Keywords: | unsymmetric orthonormality Krylov subspace convergence IGMRES IOM GMRES |
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