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Preconditioned iterative method of solving linear equations

Author: BaiYuQin
Tutor: HuangTingZhu
School: University of Electronic Science and Technology
Course: Computational Mathematics
Keywords: L- matrix H - matrix M - matrix Preconditioned AOR method SSOR multisplitting
CLC: O241.6
Type: Master's thesis
Year: 2009
Downloads: 201
Quote: 1
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Abstract


With the development of the computer , in many practical applications and mathematical research , often encountered in solving linear equations , numerical algebra has become a powerful tool to deal with these issues . In this paper , the main research several pre- conditions for iterative solution of linear equations . Preconditioner to accelerate the convergence of the iterative method commonly used method , preconditioned iterative method for solving the coefficient matrix is a large sparse matrix better results . Proved when the coefficient matrix of the linear equations A preconditioned AOR irreducible L- matrix method , and prove its convergence Finally, numerical experiments verify the theoretical results . When selecting optimal parameters through numerical experiments , the obtained spectral radius of the iteration matrix can be seen . Proposed The SSOR multi- split as an internal division relaxation unsteady over two -secession law , and then study the proposed method in the solution when the coefficient matrix of this method is given for H - the convergence of the matrix of the linear system , the last specific convergence demonstrate its application . Specific instance of the data , we can see that the SSOR multisplitting method faster than the relaxation select a set of approximate optimal parameters , the convergence rate of the proposed method .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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