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Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem

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Abstract

This paper considers the mixed least squares-scaled total least squares (MLSSTLS) problem which unifies the mixed least squares-total least squares (MTLS) problem and the scaled total least squares (STLS) problem. Firstly, we present the explicit expression of the MLSSTLS solution under some conditions. Then, the perturbation analysis and condition numbers of the MLSSTLS solution are obtained. These results can reduce to some corresponding published results of the MTLS problem and the STLS problem, respectively. Finally, numerical experiments are given to illustrate our results.

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Acknowledgements

The authors would like to thank Dr. Shaoxin Wang for some helpful discussions. We also acknowledge Professor Claude Brezinski and the anonymous referees for their valuable comments and suggestions which led to a lot of improvements to the paper.

Funding

This work was supported in part by National Natural Science Foundation of China (Grant numbers: 11601054, 11801051, 11671060); and in part by Natural Science Foundation Project of CQ CSTC (Grant numbers: cstc2016jcyjA0466, cstc2019jcyj-msxmX0075).

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  1. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, People’s Republic of China

    Pingping Zhang & Qun Wang

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  1. Pingping Zhang
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  2. Qun Wang
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Correspondence to Pingping Zhang.

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Zhang, P., Wang, Q. Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem. Numer Algor 89, 1223–1246 (2022). https://doi.org/10.1007/s11075-021-01151-4

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