The QLY least-squares and the QLY least-squares minimal-norm of linear dual least squares problems

ABSTRACT

In this paper, we define a QLY total order $\stackrel{Q}{\le }$ over ${\mathbb{D}}_m$ to compare the magnitude of dual vectors. Then we consider the QLY least-squares problem and give its compact formula. Meanwhile, by comparing with a least-squares and the least-squares minimal-norm solutions, we can investigate a QLY least-squares and the QLY least-squares minimal-norm of linear dual least-squares problems. In particular, in the presence of a least-squares solution, we can get a QLY least-squares solution to be more accurate than a least-squares solution under the QLY total order.

KEYWORDS:

• Dual matrix
• dual Moore–Penrose generalized inverse
• QLY total order
• QLY least-squares
• QLY least-squares minimal-norm

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 15A10
• 15B33

Acknowledgments

The authors are very thankful to the handling editor and two anonymous referees for providing many useful comments and suggestions, which greatly improved the presentation of the article. We would like to thank Prof. Eric Chu for his carefully reading our revision.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

H. Wang is supported partially by Research Fund Project of Guangxi Minzu University under grant 2019KJQD03, Guangxi Natural Science Foundation under grant 2018GXNSFDA281023 and Thousands of Young and Middle-aged Key Teachers Training Programme in Guangxi Colleges and Universities under grant GUIJIAOSHIFAN2019-81HAO. C. Cui is supported by the Innovation Project of Guangxi Graduate Education under grant YCSW2022243. Y. Wei is supported by Innovation Program of Shanghai Municipal Education Commission, the National Natural Science Foundation of China under grant 12271108 and Shanghai Municipal Science and Technology Commission under grant 23WZ2501400.