Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations

ZHANG Wen-zhi; HUANG Pei-yan

doi:10.3879/j.issn.1000-0887.2013.07.008

Volume 34 Issue 7

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ZHANG Wen-zhi, HUANG Pei-yan. Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations[J]. Applied Mathematics and Mechanics, 2013, 34(7): 736-741. doi: 10.3879/j.issn.1000-0887.2013.07.008

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Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations

doi: 10.3879/j.issn.1000-0887.2013.07.008

School of Civil and Transportation Engineering, South China University of Technology, Guangzhou 510640, P.R.China

Received Date: 2013-05-20
Rev Recd Date: 2013-06-03
Publish Date: 2013-07-15

Abstract

Abstract

A precise iterative refinement of solution for ill-conditioned systems of linear algebraic equations was proposed. First, the ill-conditioned matrix was improved through introduction of a small parametrr, and then via the precise integration method, a highly precise method was provided for the inversion of the improved matrix. Both the theoretical convergence analysis and numerical examples show the efficiency and accuracy of the method.
- ill-conditioned linear systems,
- precise integration method (PIM),
- iterative method

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References

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