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Journal of Engineering Mathematics

, Volume 93, Issue 1, pp 99–112 | Cite as

Vector extrapolation applied to truncated singular value decomposition and truncated iteration

  • A. Bouhamidi
  • K. Jbilou
  • L. Reichel
  • H. Sadok
  • Z. Wang
Article

Abstract

This paper is concerned with the computation of accurate approximate solutions of linear systems of equations and linear least-squares problems with a very ill-conditioned matrix and error-contaminated data. The solution of these kinds of problems requires regularization. Common regularization methods include truncated singular value decomposition (TSVD) and truncated iteration with a Krylov subspace method. It can be difficult to determine when to truncate. Recently, it has been demonstrated that extrapolation of approximate solutions determined by TSVD gives a new sequence of approximate solutions that is less sensitive to errors in data than the original approximate solutions. The present paper describes a novel approach to determining a suitable truncation index by comparing the original and extrapolated approximate solutions. Applications to TSVD and the LSQR iterative method are presented.

Keywords

Discrete ill-posed problem LSQR Truncation criterion Truncated iteration  Truncated singular value decomposition Vector extrapolation 

Notes

Acknowledgments

This research was supported in part by National Science Foundation Grant DMS-1115385. The research was also supported by the Jiangsu Oversea Research & Training Program for Prominent Young & Middle-Aged University Teachers and Presidents and the Fundamental Research Funds for Central Universities Grant NZ2012307.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • A. Bouhamidi
    • 1
  • K. Jbilou
    • 1
  • L. Reichel
    • 2
  • H. Sadok
    • 1
  • Z. Wang
    • 3
  1. 1.Laboratoire de Mathématiques Pures et Appliquées, Centre Universtaire de la Mi-VoixUniversité du Littoral Calais CedexFrance
  2. 2.Department of Mathematical SciencesKent State UniversityKentUSA
  3. 3.Department of Mathematics, College of ScienceNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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