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 Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 2, Pages 63–73 (Mi timm1059)

Separate reconstruction of solution components with singularities of various types for linear operator equations of the first kind

V. V. Vasinab, E. O. Sobolevaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b B. N. Yeltsin Ural Federal University

Abstract: A linear operator equation of the first kind is investigated. The solution of this equation contains singularities of various types; namely, along with a smooth background, the solution has sharp bends and jump discontinuities. For the construction of a stable approximated solution, a modified Tikhonov method with a stabilizer in the form of the sum of three functionals is proposed. Each of the functionals accounts for the specific character of the corresponding component of the solution. Convergence theorems are formulated, the general discrete approximation scheme of the regularizing algorithm is justified, and results of numerical experiments are discussed.

Keywords: Tikhonov method, ill-posed problem, solution with singularities, regularizing algorithm.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 289, suppl. 1, 216–226

Bibliographic databases:

UDC: 517.983.54

Citation: V. V. Vasin, E. O. Soboleva, “Separate reconstruction of solution components with singularities of various types for linear operator equations of the first kind”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 63–73; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 216–226

Citation in format AMSBIB
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This publication is cited in the following articles:
1. V. V. Vasin, “Regularization of Ill-Posed Problems By Using Stabilizers in the Form of the Total Variation of a Function and Its Derivatives”, J. Inverse Ill-Posed Probl., 24:2 (2016), 149–158
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