A note on the pin-pointing solution of ill-conditioned linear system of equations

Abstract

Volokh and Vilnay [Appl. Math. Lett. 13 (2000), pp. 119–124] proposed a method for computing an accurate solution of nearly singular linear systems of equations. The method is processed in two stages. Their method uses the truncated singular value decomposition of the initial coefficient matrix at the first stage and the Gaussian elimination procedure for well-conditioned reduced system of linear equations at the second stage. In this note, we propose a multistage approach based on the Volokh and Vilnay's method. Some numerical results are given to show the efficiency of the proposed method.

Keywords:

• linear system
• ill-conditioned
• SVD
• nullspace
• multistage

AMS Subject Classification: :

• 65F22

Acknowledgements

The authors would like to thank the referee for his (or her) helpful comments.