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Titlebook: New Trends in Parameter Identification for Mathematical Models; Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli Book 2018 Springer Internati

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On Nonstationary Iterated Tikhonov Methods for Ill-Posed Equations in Banach Spaces,y, the Lagrange multipliers) for the nIT iteration, aiming to obtain a fast decay of the residual..Numerical experiments are presented for a 1D convolution problem (smooth Tikhonov functional and Banach parameter-space), and for a 2D deblurring problem (nonsmooth Tikhonov functional and Hilbert parameter-space).
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Modification of Iterative Tikhonov Regularization Motivated by a Problem of Identification of Laser initial problem to that of finding an approximation of the function in a class of functions whose minimum can easily be calculated. The presented method is motivated by a problem of identification of laser beam quality parameters, however the scope of its applicability is quite general.
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On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods,the dimension of subspaces as the regularization parameter. Convergence conditions are also given for the choice of the dimension by the discrepancy principle, without the requirement that the projection operators are uniformly bounded.
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