Geodesic
Conditions of sourcewise representability and power estimates of convergence rate in Tikhonov's scheme for solving ill-posed extremal problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 72-82

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We investigate rate of convergence estimates for approximations generated by Tikhonov's scheme for solving ill-posed optimization problems with general smooth functionals in a Hilbert space. Sourcewise representability conditions necessary and sufficient for convergence of approximations at the power rate are established. Sufficient conditions are related to estimates of a discrepancy by the objective functional while necessary ones are formulated for estimates by the argument. The cases are specified where sufficient and necessary conditions coincide in the main.
Keywords: ill-posed optimization problem, Hilbert space, Tikhonov's scheme, rate of convergence, sourcewise representability condition. 
M. Yu. Kokurin. Conditions of sourcewise representability and power estimates of convergence rate in Tikhonov's scheme for solving ill-posed extremal problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 72-82. http://geodesic.mathdoc.fr/item/IVM_2014_7_a6/
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     title = {Conditions of sourcewise representability and power estimates of convergence rate in {Tikhonov's} scheme for solving ill-posed extremal problems},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2014_7_a6/}
}
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