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Small sample statistical condition estimation for the total least squares problem

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Abstract

In this paper, under the genericity condition, we study the condition estimation of the total least squares (TLS) problem based on small sample condition estimation (SCE), which can be incorporated into the direct solver for the TLS problem via the singular value decomposition (SVD) of the augmented matrix [A, b]. Our proposed condition estimation algorithms are efficient for the small and medium size TLS problem because they utilize the computed SVD of [A, b] during the numerical solution to the TLS problem. Numerical examples illustrate the reliability of the algorithms. Both normwise and componentwise perturbations are considered. Moreover, structured condition estimations are investigated for the structured TLS problem.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Huai-An Diao

  2. School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Yimin Wei

  3. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, People’s Republic of China

    Pengpeng Xie

Authors
  1. Huai-An Diao
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  2. Yimin Wei
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  3. Pengpeng Xie
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Correspondence to Huai-An Diao.

Additional information

Dedicated to Prof. Ken Hayami on occasions of his 60th birthday

H. Diao is supported by National Natural Science Foundation of China. Y. Wei is supported by National Natural Science Foundation of China under grant 11271084. P. Xie is supported by the Fundamental Research Funds for the Central Universities under grant 201562012.

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Diao, HA., Wei, Y. & Xie, P. Small sample statistical condition estimation for the total least squares problem. Numer Algor 75, 435–455 (2017). https://doi.org/10.1007/s11075-016-0185-9

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  • DOI: https://doi.org/10.1007/s11075-016-0185-9

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