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2008•Journal of Shandong UniversityRequires access

The parallel row action method with the greedy method for the system of linear equations

LI An-zhi

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Abstract

The Gram-Schmidt's orthogonalization,row action method with the greedy method and dividing-conquering strategy were used to put forth a parallel numerical method of solving an arbitrary system of linear algebraic equations.It was proved that this method is convergent to the arbitrary consistent system of linear algebraic equations.Its computational complexity and numerical stability were analyzed,and its application prospects in the study of a message passing parallel algorithm for a system of linear algebraic equations were discussed.

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What this paper is about

The Gram-Schmidt's orthogonalization,row action method with the greedy method and dividing-conquering strategy were used to put forth a parallel numerical method of solving an arbitrary system of linear algebraic equations.It was proved that this method is convergent to the arbitrary consistent system of linear algebraic equations.Its computational complexity and numerical stability were analyzed,and its application prospects in the study of a message passing parallel algorithm for a system of linear algebraic equations were discussed.

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Available abstract

The Gram-Schmidt's orthogonalization,row action method with the greedy method and dividing-conquering strategy were used to put forth a parallel numerical method of solving an arbitrary system of linear algebraic equations.It was proved that this method is convergent to the arbitrary consistent system of linear algebraic equations.Its computational complexity and numerical stability were analyzed,and its application prospects in the study of a message passing parallel algorithm for a system of linear algebraic equations were discussed.

Key concepts: Orthogonalization, Algebraic equation, System of linear equations, Mathematics, Action (physics), Linear equation, Linear system, Stability (learning theory)

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