Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems

By Misha Elena Kilmer, Dianne P. O'Leary. SIAM Journal on Matrix Analysis and Applications, 2000

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Arnoldi-Tikhonov regularization methods (2009, methodology): “Many available methods for the solution of large-scale Tikhonov regularization problems (4) are based on the Lanczos bidiagonalization process instead of the Arnoldi process; see, e.g., Bj¨orck [3], Calvetti et al. [8,9], Golub and von Matt [14], Kilmer and O’Leary [ 21 ], O’Leary and Simmons [24], ”
On Lanczos Based Methods for the Regularization of Discrete Ill-Posed Problems (2001, methodology): “Recent work on hybrid methods ([3, 14 ], see also [8, 13, 7]) has mostly been focused on the choice of appropriate regularization parameters, i.e., the stopping index k for the Lanczos process and the truncation index l for the embedded tsvd regularization.”
Fully Probe-Corrected Near-Field Far-Field Transformation Employing Plane Wave Expansion and Diagonal Translation Operators (2008, background): “The small singular values of an ill-posed matrix magnify the unavoidable additive noise of the measured near-field values [23].”
Structural damage detection by a new iterative regularization method and an improved sensitivity function (2017, methodology): “The most common methods for the determination of regularization parameter are discrepancy principle, generalized cross-validation (GCV) and L-curve [43].”