Total least squares problem with the arbitrary unitarily invariant norms

Abstract

This paper is focused on the total least squares (TLS) minimization of an approximation problem , with multiple right-hand sides. We consider the minimization with respect to a general unitarily invariant norm (UIN). In particular, we investigate existence of the TLS solution, relationships among TLS solutions with respect to different UINs, uniqueness of the correction matrices and of the TLS solution.

Keywords:

• Total least squares
• unitarily invariant norms
• symmetric gauge function
• singular value decomposition

AMS Subject Classifications:

• 15A18
• 15A60
• 65F20
• 65F35

Acknowledgements

I am grateful to the two anonymous referees for useful comments and suggestions which greatly improve this paper.

Notes

No potential conflict of interest was reported by the author.

1 For , we will write either or whichever is more convenient.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11371333/A011705]; Shandong Province Natural Science Foundation [ZR2013AM025].