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On convergence criteria for approximations to regularization methods

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References

  1. A. N. Tikhonov, “On the regularization of ill-posed problems,” Dokl. Akad. Nauk,153, No. 1, 49–52 (1963).

    Google Scholar 

  2. M. M. Lavrent'ev, On Some Ill-Posed Problems of Mathematical Physics [in Russian], Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1962).

    Google Scholar 

  3. V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and Its Applications [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  4. V. V. Vasin and V. P. Tanana, “Necessary and sufficient conditions of convergence of projection methods for linear unstable problems,” Dokl. Akad. Nauk SSSR,215, No. 5, 1032–1034 (1974).

    MathSciNet  Google Scholar 

  5. V. V. Vasin, “Discrete convergence and finite-dimensional approximation of regularized algorithms,” Zh. Vychisl. Mat. i Mat. Fiz.,19, No. 1, 11–21 (1979).

    MATH  MathSciNet  Google Scholar 

  6. V. V. Vasin, Methods for Solving Unstable Problems [in Russian], Ural'sk. Univ., Sverdlovsk (1989).

    Google Scholar 

  7. V. P. Tanana, Methods for Solving Operator Equations [in Russian], Nauka, Moscow (1981).

    MATH  Google Scholar 

  8. M. G. Gol'dina and V. P. Tanana, “Finite-dimensional approximation by the residual method inE-spaces,” in: Studies in Functional Analysis and Its Applications [in Russian], Ural'sk. Univ., Sverdlovsk, 1985, pp. 9–18.

    Google Scholar 

  9. H. H. Schaefer, Topological Vector Spaces [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  10. V. P. Tanana, “A criterion for convergence of approximations in the residual method for linear ill-posed problems,” J. Inverse Ill-Posed Probl.,5, No. 2, 2–12 (1997).

    Article  MathSciNet  Google Scholar 

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Chelyabinsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 1, pp. 130–141, January–February, 1999.

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Menikhes, L.D., Tanana, V.P. On convergence criteria for approximations to regularization methods. Sib Math J 40, 110–120 (1999). https://doi.org/10.1007/BF02674297

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  • DOI: https://doi.org/10.1007/BF02674297

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