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The solution of linear operator equations by the method of nonstationary approximation of the inverse operator

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Literature cited

  1. S. Ul'm, “On iteration methods with sequential approximation of the inverse operator,” Izv. Akad. Nauk ÉSSR, Fiz. Matem.,16, No. 4 (1967).

  2. O. Vaarman, “On some iteration methods with sequential approximation of the inverse operator,” Izv. Akad. NaukÉSSR, Fiz. Matem.,19, No. 1 (1969).

  3. O. Vaarman, “On the use of generalized inverse operators and their approximations for the solution of nonlinear equations,” Izv. Akad. NaukÉSSR, Fiz. Matem.,19, No. 3 (1970).

  4. V. M. Verbzhitskii and Z. B. Tsalyuk, “On the strengthened method of Newton-Kantorovich with approximations of the inverse operator,” ZhVM i MF,4, No. 6 (1964).

  5. A. B. Bakushinskii, “A method for numerical solution of integral equations,” in: Computational Methods and Programming [in Russian], No. 3, Izd. MGU, Moscow (1965).

    Google Scholar 

  6. G. Schulz, “Iterative Berechnung der reziproken Matrix,” Z. Ang. Math. Mech.,13, 57–59 (1933).

    Google Scholar 

  7. W. V. Petryshyn, “On the inversion of matrices and linear operators,” Proc. Amer. Math. Soc.,16, No. 5, 893–901 (1965).

    Google Scholar 

  8. T. S. Kravchuk (Kurchenko) and L. V. Vakulenko (Svetal‘c’ka), “Approximation of an invertible linear operator with the help of nonstationary algorithms,” Dokl. Akad. Nauk URSR, Ser, A, No. 7 (1973).

  9. L. Collatz, Functional Analysis and Numerical Mathematics [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  10. T. Kato, Theory of Perturbed Linear Operators [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  11. M. Altman, “An optimum cubically convergent iterative method of inverting a linear bounded operator in Hilbert spaces,” Pacific J. Math.,10, No. 4, 1107–1113 (1960).

    Google Scholar 

  12. M. A. Krasnosel'skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  13. L. V. Kantorovich and V. I. Krylov, Approximation Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 27, No. 4, pp. 534–540, July–August, 1975.

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Kurchenko, T.S., SvetaL'skaya, L.V. The solution of linear operator equations by the method of nonstationary approximation of the inverse operator. Ukr Math J 27, 438–443 (1975). https://doi.org/10.1007/BF01085595

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  • DOI: https://doi.org/10.1007/BF01085595

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