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On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method

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References

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

    Google Scholar 

  2. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  5. A. B. Bakushinskiî and A. V. Goncharskiî, Ill-Posed Problems. Numerical Methods and Applications [in Russian], Moscow Univ., Moscow (1989).

    Google Scholar 

  6. Ya. I. Al'ber and I. P. Ryazantseva, “The residual principle for solving nonlinear problems with monotone operators is a regularization algorithm,” Dokl. Akad. Nauk SSSR,239, No. 5, 1017–1020 (1978).

    Google Scholar 

  7. V. A. Morozov, “Solving functional equations by the regularization method,” Dokl. Akad. Nauk SSSR,167, No. 3, 510–512 (1966).

    Google Scholar 

  8. V. A. Morozov, “On regularization of ill-posed problems and selection of the regularization parameter,” Zh. Vychisl. Mat. i Mat. Fiz.,6, No. 1, 170–175 (1966).

    Google Scholar 

  9. A. N. Tikhonov and V. B. Glasko, “Application of the regularization method to nonlinear problems,” Zh. Vychisl. Mat. i Mat. Fiz.,5, No. 3, 93–107 (1965).

    Google Scholar 

  10. A. B. Bakushinskiî, “Remark on selection of the regularization parameter to the criterion of quasioptimality and ratio,” Zh. Vychisl. Mat. i Mat. Fiz.,24, No. 8, 1258–1259 (1984).

    Google Scholar 

  11. A. S. Leonov, “On solving linear ill-posed problems on the basis of the modified criterion for quasioptimality,” Mat. Sb.,122 (164), No. 3(11), 405–415 (1983).

    Google Scholar 

  12. F. P. Vasil'ev, Numerical Methods for Solving Extremal Problems [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  13. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  14. A. S. Leonov, “On accuracy of the Tikhonov regularization algorithms and quasioptimum selection of the regularization parameter,” Dokl. Akad. Nauk SSSR,321, No. 3, 460–465 (1991).

    Google Scholar 

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Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 4, pp. 117–126, July–August, 1993.

Translated by S. G. Pyatkov

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Leonov, A.S. On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method. Sib Math J 34, 695–703 (1993). https://doi.org/10.1007/BF00975172

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  • DOI: https://doi.org/10.1007/BF00975172

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