A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations |
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Authors: | Zhong‐Zhi Bai |
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Institution: | (1) State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, PR China |
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Abstract: | A class of modified block SSOR preconditioners is presented for solving symmetric positive definite systems of linear equations,
which arise in the hierarchical basis finite element discretizations of the second order self‐adjoint elliptic boundary value
problems. This class of methods is strongly related to two level methods, standard multigrid methods, and Jacobi‐like hierarchical
basis methods. The optimal relaxation factors and optimal condition numbers are estimated in detail. Theoretical analyses
show that these methods are very robust, and especially well suited to difficult problems with rough solutions, discretized
using highly nonuniform, adaptively refined meshes.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | symmetric positive definite linear system block SSOR iteration preconditioner hierarchical basis discretization 65F10 65N20 CR: G1 8 |
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