Abstract
We present a projection-based iterative algorithm for computing general-form Tikhonov regularized solutions to the problem min x{∥Ax:- b∥22+λ2∥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 language | English (US) |
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Pages (from-to) | 315-330 |
Number of pages | 16 |
Journal | SIAM Journal on Scientific Computing |
Volume | 29 |
Issue number | 1 |
DOIs | |
State | Published - 2007 |
Externally published | Yes |
Keywords
- General-form Tikhonov regularization
- Iterative bidiagonalization methods
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics