Computational Statistics & Data Analysis
An Efficient Iterative Approach for Large-Scale Separable Nonlinear Inverse Problems
SIAM Journal on Scientific Computing
Multilevel Approach For Signal Restoration Problems With Toeplitz Matrices
SIAM Journal on Scientific Computing
Tikhonov regularization based on generalized Krylov subspace methods
Applied Numerical Mathematics
Preconditioning linear systems via matrix function evaluation
Applied Numerical Mathematics
Automatic parameter setting for Arnoldi-Tikhonov methods
Journal of Computational and Applied Mathematics
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We present a projection-based iterative algorithm for computing general-form Tikhonov regularized solutions to the problem $\min_x\{\| Ax-b \|_2^2+\lambda^2\| Lx \|_2^2\}$, where the regularization matrix $L$ is not the identity. Our algorithm is designed for the common case where $\lambda$ 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.