Geodesic
Separate reconstruction of solution components with singularities of various types for linear operator equations of the first kind
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 63-73

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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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     author = {V. V. Vasin and E. O. Soboleva},
     title = {Separate reconstruction of solution components with singularities of various types for linear operator equations of the first kind},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {63--73},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a5/}
}
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 63-73. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a5/