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This article is cited in 15 scientific papers (total in 16 papers)
Approximation of nonsmooth solutions of linear ill-posed problems
V. V. Vasin
Abstract:
In the multidimensional case, for the Tikhonov regularization, two new families of stabilizers containing the norms of the Lipschitz spaces and the norms of the Sobolev spaces with fractional derivatives are suggested. Theorems of convergence of Tikhonov regularized approximate solutions and their discrete approximations are proved. Detailed step-by-step investigation of the solving algorithm is performed by the example of an integral Fredholm equation of the first kind.
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Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 253, suppl. 1, S247–S262
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517.983.54
Received: 11.01.2006
Citation:
V. V. Vasin, “Approximation of nonsmooth solutions of linear ill-posed problems”, Dynamical systems: modeling, optimization, and control, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 1, 2006, 64–77; Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S247–S262
Citation in format AMSBIB
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\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\pages 64--77
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
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\pages S247--S262
\crossref{https://doi.org/10.1134/S008154380605018X}
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http://mi.mathnet.ru/eng/timm134 http://mi.mathnet.ru/eng/timm/v12/i1/p64
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Korotkii M.A., “The reconstruction of controls by regularization methods with uneven stabilizers”, J. Appl. Math. Mech., 73:1 (2009), 26–35
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A. I. Korotkii, D. O. Mikhailova, “Vosstanovlenie upravlenii v parabolicheskikh sistemakh metodom Tikhonova s negladkimi stabilizatorami”, Tr. IMM UrO RAN, 16, no. 4, 2010, 211–227
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Vasin V.V., Serëzhnikova T.I., “Regulyarnyi algoritm approksimatsii negladkikh reshenii dlya integralnykh uravnenii Fredgolma pervogo roda”, Vychislitelnye tekhnologii, 15:2 (2010), 15–23
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Serëzhnikova T.I., “O regulyarnom algoritme vosstanovleniya negladkikh reshenii integralnykh uravnenii Fredgolma pervogo roda”, Voprosy atomnoi nauki i tekhniki. Ser.: Matematicheskoe modelirovanie fizicheskikh protsessov, 2010, no. 4, 71–78
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T. I. Serezhnikova, “O metode regulyarizatsii dlya vosstanovleniya negladkogo resheniya dvumernogo integralnogo uravneniya pervogo roda”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 2, Modelirovanie i optimizatsiya dinamicheskikh sistem i sistem s raspredelennymi parametrami, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 233–236
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A. I. Korotkii, E. I. Gribanova, “Reconstruction of controls in hyperbolic systems by Tikhonov's method with nonsmooth stabilizers”, Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S68–S77
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Vasin V., Skorik G., “Iterative processes of gradient type with applications to gravimetry and magnetometry inverse problems”, J. Inverse Ill Posed Probl., 18:8 (2011), 855–876
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T. I. Serezhnikova, “Ustoichivye metody vosstanovleniya zashumlennykh izobrazhenii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 9, 32–42
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A. I. Korotkii, E. I. Gribanova, “Control reconstruction in hyperbolic systems”, Autom. Remote Control, 73:3 (2012), 472–484
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“Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12
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A. I. Korotkii, D. O. Mikhailova, “Reconstruction of boundary controls in parabolic systems”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 98–118
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A. S. Leonov, “Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 119–133
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A. I. Korotkii, E. I. Gribanova, “Vosstanovlenie granichnykh upravlenii v giperbolicheskikh sistemakh”, Tr. IMM UrO RAN, 18, no. 2, 2012, 154–169
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I. A. Tsepelev, “Approksimatsiya negladkikh reshenii retrospektivnoi zadachi dlya modeli konvektsii-diffuzii”, Tr. IMM UrO RAN, 18, no. 2, 2012, 281–290
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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”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 216–226
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Vasin V.V., “Approximation of Solutions with Singularities of Various Types for Linear Ill-Posed Problems”, Dokl. Math., 89:1 (2014), 30–33
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