Regularized Total Least Squares: Computational Aspects and Error Bounds

  • Authors:

  • Shuai Lu;Sergei V. Pereverzev;Ulrich Tautenhahn

  • Affiliations:

  • -;shuai.lu@oeaw.ac.at and sergei.pereverzyev@oeaw.ac.at;u.tautenhahn@hs-zigr.de

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 2009

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Abstract

For solving linear ill-posed problems, regularization methods are required when the right-hand side and/or the operator are corrupted by some noise. In the present paper, regularized solutions are constructed using regularized total least squares (RTLS) and dual regularized total least squares (DRTLS). We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, DRTLS, and the standard Tikhonov regularization.