Remarks on choosing a regularization parameter using the quasioptimality and ratio criterion
USSR Computational Mathematics and Mathematical Physics
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
The triangle method for finding the corner of the L-curve
Applied Numerical Mathematics
Iterative methods for ill-posed problems and semiconvergent sequences
Journal of Computational and Applied Mathematics
An adaptive pruning algorithm for the discrete L-curve criterion
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
A new L-curve for ill-posed problems
Journal of Computational and Applied Mathematics
Matrices, Moments and Quadrature with Applications
Matrices, Moments and Quadrature with Applications
Original Article: Comparingparameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Automatic parameter setting for Arnoldi-Tikhonov methods
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Linear discrete ill-posed problems are difficult to solve numerically because their solution is very sensitive to perturbations, which may stem from errors in the data and from round-off errors introduced during the solution process. The computation of a meaningful approximate solution requires that the given problem be replaced by a nearby problem that is less sensitive to disturbances. This replacement is known as regularization. A regularization parameter determines how much the regularized problem differs from the original one. The proper choice of this parameter is important for the quality of the computed solution. This paper studies the performance of known and new approaches to choosing a suitable value of the regularization parameter for the truncated singular value decomposition method and for the LSQR iterative Krylov subspace method in the situation when no accurate estimate of the norm of the error in the data is available. The regularization parameter choice rules considered include several L-curve methods, Regińska's method and a modification thereof, extrapolation methods, the quasi-optimality criterion, rules designed for use with LSQR, as well as hybrid methods.