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2012•Applied Mechanics and MaterialsOpen access

Modified Block Symmetric SOR Preconditioners for Large Sparse Saddle-Point Problems

Li Tao Zhang, Shao Hua Cheng

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Abstract

In this paper, based on the preconditioners presented by Wang [On hybrid preconditioning methods for large sparse saddle-point problems, Linear Algebra Appl., 434 (2011) 2353-2366], we introduce and study the block symmetric SOR (BSSOR) and the modified block symmetric SOR (MBSSOR) preconditioners for the block traingular product approximation to a 2-by-2 block matrix and these preconditioners are the generalization of BSGS and MBSGS preconditioners presented by Wang. Moreover, we analyse the properties of the corresponding preconditioned matrices.

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In this paper, based on the preconditioners presented by Wang [On hybrid preconditioning methods for large sparse saddle-point problems, Linear Algebra Appl., 434 (2011) 2353-2366], we introduce and study the block symmetric SOR (BSSOR) and the modified block symmetric SOR (MBSSOR) preconditioners for the block traingular product approximation to a 2-by-2 block matrix and these preconditioners are the generalization of BSGS and MBSGS preconditioners presented by Wang. Moreover, we analyse the properties of the corresponding preconditioned matrices.

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Available abstract

In this paper, based on the preconditioners presented by Wang [On hybrid preconditioning methods for large sparse saddle-point problems, Linear Algebra Appl., 434 (2011) 2353-2366], we introduce and study the block symmetric SOR (BSSOR) and the modified block symmetric SOR (MBSSOR) preconditioners for the block traingular product approximation to a 2-by-2 block matrix and these preconditioners are the generalization of BSGS and MBSGS preconditioners presented by Wang. Moreover, we analyse the properties of the corresponding preconditioned matrices.

Key concepts: Saddle point, Block (permutation group theory), Mathematics, Generalization, Applied mathematics, Matrix (chemical analysis), Saddle, Algorithm

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