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Dokl. Akad. Nauk SSSR, 1963, Volume 153, Number 1, Pages 49–52 (Mi dan28764)  

This article is cited in 37 scientific papers (total in 39 papers)

MATHEMATICS

On the regularization of ill-posed problems

A. N. Tikhonov


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Bibliographic databases:
Received: 15.08.1963

Citation: A. N. Tikhonov, “On the regularization of ill-posed problems”, Dokl. Akad. Nauk SSSR, 153:1 (1963), 49–52

Citation in format AMSBIB
\Bibitem{Tik63}
\by A.~N.~Tikhonov
\paper On the regularization of ill-posed problems
\jour Dokl. Akad. Nauk SSSR
\yr 1963
\vol 153
\issue 1
\pages 49--52
\mathnet{http://mi.mathnet.ru/dan28764}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0162378}
\zmath{https://zbmath.org/?q=an:0183.11601}


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    Citing articles on Google Scholar: Russian citations, English citations
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    1. V. A. Il'in, “Tikhonov's work on methods of solving ill-posed problems”, Russian Math. Surveys, 22:2 (1967), 142–149  mathnet  crossref  mathscinet  zmath
    2. “Spisok pechatnykh rabot A. N. Tikhonova”, UMN, 22:2(134) (1967), 185–188  mathnet  mathscinet
    3. A. L. Bukhgeim, “On a class of Volterra equations of the first kind”, Funct. Anal. Appl., 6:1 (1972), 1–8  mathnet  crossref  mathscinet  zmath
    4. A. M. Fedotov, “Minimax regularization for operator equations with random errors in the data”, Comput. Math. Math. Phys., 32:4 (1992), 423–432  mathnet  mathscinet  zmath  isi
    5. E. N. Domanskii, “On Maslov regularizability of discontinuous mappings”, Russian Acad. Sci. Izv. Math., 42:1 (1994), 27–49  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. E. N. Domanskii, “Sequential regularizability in the sense of Maslov for improperly posed problems”, Math. Notes, 56:4 (1994), 1036–1042  mathnet  crossref  mathscinet  zmath  isi
    7. A. V. Goncharsky, S. Yu. Romanov, “On a three-dimensional problem of diagnostics in the wave approximation”, Comput. Math. Math. Phys., 40:9 (2000), 1308–1311  mathnet  mathscinet  zmath
    8. P. A. Savenko, “Numerical solution of a class of nonlinear problems in synthesis of radiating systems”, Comput. Math. Math. Phys., 40:6 (2000), 889–899  mathnet  mathscinet  zmath
    9. V. P. Tanana, A. A. Shtarkman, “O skhodimosti konechnomernykh approksimatsii $L$-regulyarizovannykh reshenii”, Sib. zhurn. vychisl. matem., 3:4 (2000), 395–403  mathnet  zmath
    10. A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the application of Craig's method to the solution of linear equations with inexact initial conditions”, Comput. Math. Math. Phys., 42:12 (2002), 1693–1700  mathnet  mathscinet  zmath
    11. A. P. Khromov, G. V. Khromova, “Extension of the convergence domain in the Tikhonov method”, Comput. Math. Math. Phys., 42:8 (2002), 1067–1072  mathnet  mathscinet  zmath  elib
    12. G. V. Khromova, “Tikhonov's method and approximation of periodic functions”, Comput. Math. Math. Phys., 43:4 (2003), 489–493  mathnet  mathscinet  zmath
    13. A. V. Bokov, V. P. Tanana, “O regulyarizatsii nelineinykh operatornykh uravnenii”, Vestnik ChelGU, 2003, no. 7, 5–21  mathnet
    14. G. V. Khromova, “On the Tikhonov regularization in spaces of differentiable functions”, Comput. Math. Math. Phys., 44:4 (2004), 547–551  mathnet  mathscinet  zmath
    15. A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the implementation of an elimination method in linear problems with inexactly specified initial data”, Comput. Math. Math. Phys., 44:4 (2004), 604–613  mathnet  mathscinet  zmath
    16. G. V. Khromova, “On the moduli of continuity of unbounded operators”, Russian Math. (Iz. VUZ), 50:9 (2006), 67–74  mathnet  mathscinet
    17. V. V. Vasin, “Approximation of nonsmooth solutions of linear ill-posed problems”, Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S247–S262  mathnet  crossref  mathscinet  zmath  elib
    18. S. Yu. Sovetnikova, G. V. Khromova, “On the regularization of an equation of the first kind with a multiple integration operator”, Comput. Math. Math. Phys., 47:4 (2007), 555–563  mathnet  crossref  mathscinet  zmath
    19. M. L. Kazaryan, “Primenenie metoda regulyarizatsii Tikhonova k zadache szhatiya signalov”, Matem. modelirovanie, 20:4 (2008), 8–26  mathnet  mathscinet  zmath
    20. V. V. Vasin, “Iterative processes of the Fejér type in ill-posed problems with a prori information”, Russian Math. (Iz. VUZ), 53:2 (2009), 1–20  mathnet  crossref  mathscinet  zmath  elib
    21. P. A. Chistyakov, “Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces”, Russian Math. (Iz. VUZ), 53:10 (2009), 72–77  mathnet  crossref  mathscinet  zmath
    22. D. A. Lavrik, A. Kh. Pergament, “Regulyarizovannye algoritmy statisticheskogo otsenivaniya funktsii”, Preprinty IPM im. M. V. Keldysha, 2009, 002, 20 pp.  mathnet
    23. A. A. Khromov, “Reshenie integralnykh uravnenii s pomoschyu rezolvent prosteishikh differentsialnykh operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:1 (2009), 52–58  mathnet  crossref
    24. E. A. Nikolaevskaya, A. N. Khimich, “Error estimation for a weighted minimum-norm least squares solution with positive definite weights”, Comput. Math. Math. Phys., 49:3 (2009), 409–417  mathnet  crossref  mathscinet  isi  elib
    25. A. A. Khromov, G. V. Khromova, “Finding approximations of continuous solutions to first-kind equations”, Comput. Math. Math. Phys., 49:2 (2009), 217–223  mathnet  crossref  mathscinet  zmath  isi
    26. N. M. Yaparova, “Ob optimalnosti metoda Tikhonova nulevogo poryadka na nekotorykh klassakh korrektnosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2009, no. 1, 13–20  mathnet
    27. M. Yu. Zaslavskii, “On interpretation of the direct current electrical prospecting measurements”, Math. Models Comput. Simul., 3:1 (2011), 9–17  mathnet  crossref  mathscinet  zmath
    28. D. A. Lavrik, I. R. Minniakhmetov, A. Kh. Pergament, “Regulyarizovannye algoritmy statisticheskogo otsenivaniya funktsii v zadachakh geologicheskogo modelirovaniya”, Matem. modelirovanie, 23:4 (2011), 23–40  mathnet  mathscinet
    29. N. A. Evdokimova, D. V. Lukyanenko, A. G. Yagola, “Vosstanovlenie orientatsionnoi funktsii raspredeleniya chastits”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 172–176  mathnet
    30. V. S. Antyufeev, “Finding the most probable non-negative solution of systems of linear algebraic equations by the likelihood method”, Num. Anal. Appl., 6:3 (2013), 187–196  mathnet  crossref  mathscinet
    31. V. F. Mirasov, A. I. Sidikova, “Priblizhennoe reshenie obratnoi granichnoi zadachi teploobmena metodom regulyarizatsii A. N. Tikhonova”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:2 (2014), 5–11  mathnet
    32. O. I. Shatalina, “O priblizhenii i vosstanovlenii nepreryvnykh funktsii s kraevymi usloviyami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 603–608  mathnet  crossref  elib
    33. A. I. Sidikova, E. Yu. Vishnyakov, A. A. Ershova, “Otsenka pogreshnosti priblizhennogo resheniya integralnogo uravneniya metodom nevyazki”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 39–47  mathnet  elib
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