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Zh. Vychisl. Mat. Mat. Fiz., 1979, Volume 19, Number 1, Pages 11–21 (Mi zvmmf5397)  

This article is cited in 8 scientific papers (total in 9 papers)

Discrete convergence and finite-dimensional approximation of regularizing algorithms

V. V. Vasin

Sverdlovsk

Abstract: For the linear operator equation of the 1st kind $Au=f$, the convergence of the general scheme of finite-dimensional approximation (discretization) of the Tikhonov-regularized family of approximate solutions is examined, along with the application of this scheme to projection and quadrative methods.

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English version:
USSR Computational Mathematics and Mathematical Physics, 1979, 19:1, 8–19

Bibliographic databases:

UDC: 519, 517.988.8
MSC: Primary 65J10; Secondary 65R20, 45L05
Received: 20.06.1977
Revised: 30.08.1977

Citation: V. V. Vasin, “Discrete convergence and finite-dimensional approximation of regularizing algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 19:1 (1979), 11–21; U.S.S.R. Comput. Math. Math. Phys., 19:1 (1979), 8–19

Citation in format AMSBIB
\Bibitem{Vas79}
\by V.~V.~Vasin
\paper Discrete convergence and finite-dimensional approximation of regularizing algorithms
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1979
\vol 19
\issue 1
\pages 11--21
\mathnet{http://mi.mathnet.ru/zvmmf5397}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=525462}
\zmath{https://zbmath.org/?q=an:0406.65027}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1979
\vol 19
\issue 1
\pages 8--19
\crossref{https://doi.org/10.1016/0041-5553(79)90062-4}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Tanana, “On the convergence of finite-dimensional approximations of regularized solutions in the theory of nonlinear problems”, Russian Math. (Iz. VUZ), 42:10 (1998), 64–68  mathnet  mathscinet  zmath  elib
    2. L. D. Menikhes, V. P. Tanana, “Konechnomernaya approksimatsiya v metode M. M. Lavrenteva”, Sib. zhurn. vychisl. matem., 1:1 (1998), 59–66  mathnet  mathscinet  zmath
    3. “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
    4. V. P. Tanana, A. I. Sidikova, “Dvustoronnyaya otsenka tochnosti regulyarizuyuschego algoritma, osnovannogo na metode M.M. Lavrenteva”, Tr. IMM UrO RAN, 21, no. 1, 2015, 238–249  mathnet  mathscinet  elib
    5. 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
    6. V. P. Tanana, S. I. Belkov, “Konechnoraznostnaya approksimatsiya metoda regulyarizatsii A.N. Tikhonova n-go poryadka”, Vestn. YuUrGU. Ser. Vych. matem. inform., 4:1 (2015), 86–98  mathnet  elib
    7. V. P. Tanana, E. Y. Vishnyakov, A. I. Sidikova, “About an approximate solution to the Fredholm integral equation of the first kind by the residual method”, Num. Anal. Appl., 9:1 (2016), 74–81  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. V. P. Tanana, A. I. Sidikova, “On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 217–224  mathnet  crossref  mathscinet  isi  elib
    9. A. I. Sidikova, “O priblizhennom reshenii odnoi obratnoi granichnoi zadachi metodom regulyarizovannogo resheniya konechnomernoi approksimatsii”, Tr. IMM UrO RAN, 23, no. 2, 2017, 210–219  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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