BIT Numerical Mathematics

, Volume 29, Issue 3, pp 491–504 | Cite as

Regularization,GSVD and truncatedGSVD

  • Per Christian Hansen
Part II Numerical Mathematics

Abstract

The purpose of this paper is to analyze Tikhonov regularization in general form by means of generalized SVD (GSVD) in the same spirit as SVD is used to analyze standard-form regularization. We also define a truncated GSVD solution which is of interest in its own right and which sheds light on regularization as well. In addition, our analysis gives insight into a particular numerical method for solving the general-form problem via a transformation to standard form.

AMS subject classification

65F20 65F30 

Keywords

Ill-posed problems regularization generalized SVD perturbation theory generalized cross-validation transformation to standard form 

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Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • Per Christian Hansen
    • 1
  1. 1.UNI·C, Building 305Technical University of DenmarkLyngbyDenmark

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