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A Two-Side Equilibration Method to Reduce the Condition Number of an Ill-Posed Linear System

Chein-Shan Liu1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2013, 91(1), 17-42. https://doi.org/10.3970/cmes.2013.091.017

Abstract

In the present paper, we propose a novel two-side equilibration method to properly reduce the condition number of a given non-singular matrix only through a few operations. Then, two different conditioners together with the conjugate gradient method (CGM) are developed, which can overcome the defect of CGM, being not vulnerable to noisy disturbance exerted on an ill-posed linear system. The twoside CGM (TSCGM) and the pre-conditioning CGM (PrCGM) are convergent fast and accurate in solving linear inverse problems and the linear Hilbert problem under a large random noise.

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Cite This Article

Liu, C. (2013). A Two-Side Equilibration Method to Reduce the Condition Number of an Ill-Posed Linear System. CMES-Computer Modeling in Engineering & Sciences, 91(1), 17–42.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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