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Solving a Type of the Tikhonov Regularization of the Total Least Squares by a New S-Lemma

  • Huu-Quang Nguyen
  • Ruey-Lin SheuEmail author
  • Yong Xia
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

We present a new S-lemma with two quadratic equalities and use it to minimize a special type of polynomials of degree 4. As a result, by the Dinkelbach approach with 2 SDP’s (semidefinite programming), the minimum value and the minimum solution to the Tikhonov regularization of the total least squares problem with \(L=I\) can be nicely obtained.

Keywords

S-lemma with equality Tikhonov regularization Total least squares Dinkelbach method 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsVinh UniversityVinhVietnam
  2. 2.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan
  3. 3.State Key Laboratory of Software Development Environment School of Mathematics and System SciencesBeihang UniversityBeijingChina

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