Efficient Computational Schemes of the Conjugate Gradient Method for Solving Linear Systems

The technique of the initial guess calculation for the conjugate gradient method is proposed. Computational schemes of the linear system solution with symmetrical positive definite matrices are constructed on its basis. Their efficient modifications for systems with five-diagonal matrices are propos...

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Bibliographic Details
Published in:Journal of computational physics 1994-02, Vol.110 (2), p.201-211
Main Authors: Mulyarchik, Stepan G., Bielawski, Stanislav S., Popov, Andrew V.
Format: Article
Language:English
Subjects:
CALCULATION METHODS 990200 > Mathematics & Computers
Computational techniques
CONVERGENCE
EFFICIENCY
Exact sciences and technology
FACTORIZATION
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ITERATIVE METHODS
Mathematical methods in physics
MATRICES
Numerical approximation and analysis
Numerical simulation, solution of equations
NUMERICAL SOLUTION
Physics
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Summary:The technique of the initial guess calculation for the conjugate gradient method is proposed. Computational schemes of the linear system solution with symmetrical positive definite matrices are constructed on its basis. Their efficient modifications for systems with five-diagonal matrices are proposed. The investigation of the developed methods using the problem of two-dimensional numerical simulation of bipolar transistors has been carried out. Experimental evidence of the proposed method's efficiency has been obtained.
ISSN:0021-9991
1090-2716
DOI:10.1006/jcph.1994.1018