Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Tikhonov regularization and the L-curve for large discrete ill-posed problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
A Projection-Based Approach to General-Form Tikhonov Regularization
SIAM Journal on Scientific Computing
Arnoldi-Tikhonov regularization methods
Journal of Computational and Applied Mathematics
Tikhonov regularization based on generalized Krylov subspace methods
Applied Numerical Mathematics
Old and new parameter choice rules for discrete ill-posed problems
Numerical Algorithms
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In the framework of iterative regularization techniques for large-scale linear ill-posed problems, this paper introduces a novel algorithm for the choice of the regularization parameter when performing the Arnoldi-Tikhonov method. Assuming that we can apply the discrepancy principle, this new strategy can work without restrictions on the choice of the regularization matrix. Moreover, this method is also employed as a procedure to detect the noise level whenever it is just overestimated. Numerical experiments arising from the discretization of integral equations and image restoration are presented.