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)
Fast CG-Based Methods for Tikhonov--Phillips Regularization
SIAM Journal on Scientific Computing
A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems
SIAM Journal on Scientific Computing
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
Tikhonov Regularization with a Solution Constraint
SIAM Journal on Scientific Computing
A Truncated Lagrange Method for Total Variation-Based Image Restoration
Journal of Mathematical Imaging and Vision
The Lagrange method for the regularization of discrete ill-posed problems
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
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In this paper, an iterative method is presented for the computation of regularized solutions of discrete ill-posed problems. In the proposed method, the regularization problem is formulated as an equality constrained minimization problem and an iterative Lagrange method is used for its solution. The Lagrange iteration is terminated according to the discrepancy principle. The relationship between the proposed approach and classical Tikhonov regularization is discussed. Results of numerical experiments are presented to illustrate the effectiveness and usefulness of the proposed method.