This article is cited in 4 papers

Conditions of sourcewise representability and power estimates of convergence rate in Tikhonov's scheme for solving ill-posed extremal problems

M. Yu. Kokurin

Chair of Mathematical Analysis and Function Theory, Mari State University, 1 Lenin sq., Ioshkar-Ola, 424000 Russia

Abstract: 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.

UDC: 517.988

Received: 29.12.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:7, 61–70

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