Open Access

ARTICLE

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

Chein-Shan Liu¹

1 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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Keywords

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