A projection-based approach to general-form Tikhonov regularization

Misha E. Kilmer, Per Christian Hansen, Malena I. Español

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


We present a projection-based iterative algorithm for computing general-form Tikhonov regularized solutions to the problem min x{∥Ax:- b∥222∥Lx∥2 2}, where the regularization matrix L is not the identity. Our algorithm is designed for the common case where λ is not known a priori. It is based on a joint bidiagonalization algorithm and is appropriate for large-scale problems when it is computationally infeasible to transform the regularized problem to standard form. By considering the projected problem, we show how estimates of the corresponding optimal regularization parameter can be efficiently obtained. Numerical results illustrate the promise of our projection-based approach.

Original languageEnglish (US)
Pages (from-to)315-330
Number of pages16
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2007
Externally publishedYes


  • General-form Tikhonov regularization
  • Iterative bidiagonalization methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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