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A contribution to perturbation analysis for total least squares problems

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Abstract

In this note, we present perturbation analysis for the total least squares (Tls) problems under the genericity condition. We review the three condition numbers proposed respectively by Zhou et al. (Numer. Algorithm, 51 (2009), pp. 381–399), Baboulin and Gratton (SIAM J. Matrix Anal. Appl. 32 (2011), pp. 685–699), Li and Jia (Linear Algebra Appl. 435 (2011), pp. 674–686). We also derive new perturbation bounds.

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Author notes

  1. Pengpeng Xie

    Present address: School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, People’s Republic of China

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Pengpeng Xie & Yimin Wei

  2. Shanghai Key Laboratory of Contemporary Applied Mathematics, Shanghai, People’s Republic of China

    Yimin Wei

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Hua Xiang

Authors
  1. Pengpeng Xie
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  2. Hua Xiang
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  3. Yimin Wei
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Corresponding author

Correspondence to Yimin Wei.

Additional information

Dedicated to the 60th Birthday of Professor Ken Hayami

P. Xie is supported by the National Natural Science Foundation of China under grant 11271084 and the Fundamental Research Funds for the Central Universities under grant 201562012. Part of the work was done when the author visited Wuhan University in 2015.

H. Xiang is supported by the National Natural Science Foundation of China under grants 11571265 and 11471253. Part of the work was completed when he visited Fudan University and The Chinese University of Hong Kong in 2015 and 2016.

Y. Wei is supported by International Cooperation Project of Shanghai Municipal Science and Technology Commission under grant 16510711200.

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Xie, P., Xiang, H. & Wei, Y. A contribution to perturbation analysis for total least squares problems. Numer Algor 75, 381–395 (2017). https://doi.org/10.1007/s11075-017-0285-1

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  • DOI: https://doi.org/10.1007/s11075-017-0285-1

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