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Trudy Inst. Mat. i Mekh. UrO RAN, 2006, Volume 12, Number 1, Pages 64–77 (Mi timm134)  

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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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 253, suppl. 1, S247–S262

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UDC: 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
\by V.~V.~Vasin
\paper Approximation of nonsmooth solutions of linear ill-posed problems
\inbook Dynamical systems: modeling, optimization, and control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 1
\pages 64--77
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 253
\issue , suppl. 1
\pages S247--S262

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    This publication is cited in the following articles:
    1. Korotkii M.A., “The reconstruction of controls by regularization methods with uneven stabilizers”, J. Appl. Math. Mech., 73:1 (2009), 26–35  crossref  mathscinet  isi  elib  scopus
    2. 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  mathnet  elib
    3. Vasin V.V., Serëzhnikova T.I., “Regulyarnyi algoritm approksimatsii negladkikh reshenii dlya integralnykh uravnenii Fredgolma pervogo roda”, Vychislitelnye tekhnologii, 15:2 (2010), 15–23  zmath  elib
    4. 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  elib
    5. 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  mathnet
    6. 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  mathnet  crossref  isi  elib
    7. 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  crossref  mathscinet  isi  elib  scopus
    8. T. I. Serezhnikova, “Ustoichivye metody vosstanovleniya zashumlennykh izobrazhenii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 9, 32–42  mathnet
    9. A. I. Korotkii, E. I. Gribanova, “Control reconstruction in hyperbolic systems”, Autom. Remote Control, 73:3 (2012), 472–484  mathnet  crossref  isi
    10. “Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12  mathnet  crossref  isi
    11. A. I. Korotkii, D. O. Mikhailova, “Reconstruction of boundary controls in parabolic systems”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 98–118  mathnet  crossref  isi  elib
    12. 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  mathnet  crossref  isi  elib
    13. A. I. Korotkii, E. I. Gribanova, “Vosstanovlenie granichnykh upravlenii v giperbolicheskikh sistemakh”, Tr. IMM UrO RAN, 18, no. 2, 2012, 154–169  mathnet  elib
    14. I. A. Tsepelev, “Approksimatsiya negladkikh reshenii retrospektivnoi zadachi dlya modeli konvektsii-diffuzii”, Tr. IMM UrO RAN, 18, no. 2, 2012, 281–290  mathnet  elib
    15. 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  mathnet  crossref  mathscinet  isi  elib
    16. Vasin V.V., “Approximation of Solutions with Singularities of Various Types for Linear Ill-Posed Problems”, Dokl. Math., 89:1 (2014), 30–33  crossref  mathscinet  zmath  isi  elib  scopus
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