Numerical Algorithms

, Volume 51, Issue 2, pp 195–208 | Cite as

Vector extrapolation enhanced TSVD for linear discrete ill-posed problems

Original Paper

Abstract

The truncated singular value decomposition (TSVD) is a popular solution method for small to moderately sized linear ill-posed problems. The truncation index can be thought of as a regularization parameter; its value affects the quality of the computed approximate solution. The choice of a suitable value of the truncation index generally is important, but can be difficult without auxiliary information about the problem being solved. This paper describes how vector extrapolation methods can be combined with TSVD, and illustrates that the determination of the proper value of the truncation index is less critical for the combined extrapolation-TSVD method than for TSVD alone. The numerical performance of the combined method suggests a new way to determine the truncation index.

Keywords

Ill-posed problem Truncated singular value decomposition Vector extrapolation Truncation criterion 

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral, Centre Universtaire de la Mi-VoixCalais cedexFrance
  2. 2.Department of Mathematical SciencesKent State UniversityKentUSA

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