On the unsolvability of inverse singular value problems almost everywhere

ABSTRACT

In this paper, the unsolvability of inverse singular value problems almost everywhere is discussed. Applying the method described by Sun and Ye [J Comput Math. 1986;4:212–226], a sufficient condition is given such that the inverse singular value problems are unsolvable almost everywhere. This result shows that inverse singular value problems are unsolvable almost everywhere if the multiplicity of zero singular values is sufficiently large.

KEYWORDS:

• Inverse singular value problem
• zero singular value
• unsolvability

AMS SUBJECT CLASSIFICATIONS:

• 65F15
• 65F99

Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was supported by National Natural Science Foundations of China [grant number 11771159], [grant number 11671158]; Major Project [2016KZDXM025]; Innovation Team Project [2015KCXTD007] of Guangdong Provincial Universities