An improved preconditioned LSQR for discrete ill-posed problems
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Robust constrained receding-horizon predictive control via bounded data uncertainties
Mathematics and Computers in Simulation
Computers & Mathematics with Applications
Computational Statistics & Data Analysis
Designing Optimal Spectral Filters for Inverse Problems
SIAM Journal on Scientific Computing
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Choosing the regularization parameter for an ill-posed problem is an art based on good heuristics and prior knowledge of the noise in the observations. In this work, we propose choosing the parameter, without a priori information, by approximately minimizing the distance between the true solution to the discrete problem and the family of regularized solutions. We demonstrate the usefulness of this approach for Tikhonov regularization and for an alternate family of solutions. Further, we prove convergence of the regularization parameter to zero as the standard deviation of the noise goes to zero.