Geodesic
Approximation of nonsmooth solutions of linear ill-posed problems
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 64-77

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In the multidimensional case, for the Tikhonov regularization, two new families of stabilizers containing the norms of the Lipschitz spaces and the norms of the Sobolev spaces with fractional derivatives are suggested. Theorems of convergence of Tikhonov regularized approximate solutions and their discrete approximations are proved. Detailed step-by-step investigation of the solving algorithm is performed by the example of an integral Fredholm equation of the first kind. 
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V. V. Vasin. Approximation of nonsmooth solutions of linear ill-posed problems. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 64-77. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a5/