Perturbation analysis of singular linear systems with index one^∗

^∗This project is supported by Doctoral Point Foundation of China, National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai, China.

Abstract

A new perturbation result for singular but consistent linear systems with coefficient matrix of index one is presented. However, if the system is inconsistent, we also derive a perturbation bound of the generalized linear least squares solution. Our treatment extends a classical perturbation result in numerical linear algebra.

Keywords:

• Singular linear system
• generalized linear least squares problem
• group inverse
• index
• Jordan canonical form

C. R. Category::

• G 1.3

^∗This project is supported by Doctoral Point Foundation of China, National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai, China.

^† [email protected]

^∗This project is supported by Doctoral Point Foundation of China, National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai, China.

^† [email protected]

Notes

^∗This project is supported by Doctoral Point Foundation of China, National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai, China.

^† [email protected]

Additional information

Notes on contributors

Yimin Wei

†