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J-fractional regularization of linear ill-posed equations

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Abstract

We present a method for solution of linear ill-posed equations in function spaces based on the use of continuousJ-fractions. We obtain a meromorphic solution of regularized equations and indicate some cases where a solution can be represented in terms of rational functions.

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References

  1. A. N. Tikhonov and V. Ya. Arsenin,Methods for Solving Ill-Posed Problems [in Russian] Nauka, Moscow 1986.

    Google Scholar 

  2. A. B. Bakushinslii and A. V. Goncharskii,Iterative Methods for Solving Ill-Posed Problems [in Russian] Nauka, Moscow 1989.

    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 1979.

    Google Scholar 

  4. M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii,Ill-Posed Problems of Mathematical Physics and Analysis [in Russian] Nauka, Moscow 1980.

    MATH  Google Scholar 

  5. B. A. Morozov,Regular Methods for Solving Ill-Posed Problems [in Russian] Nauka, Moscow 1987.

    Google Scholar 

  6. F. Natterer,The Mathematics of Computerized Tomograph, Wiley, New York 1985.

    Google Scholar 

  7. W. B. Jones and W. J. Thron,Continued Fractions, Addison-Wesley, London 1980.

    Google Scholar 

  8. G. A. Baker and P. Graves-Morris,Padé Approximants, Addison-Wesley, London 1981..

    Google Scholar 

  9. H. S. Wall,The Analytic Theory of Continued Fractions, Van Nostrand, New York 1948.

    Google Scholar 

  10. A. F. Verlan’ and V. S. Sizikov,Integral Equations: Methods, Algorithms, Programs. Reference Book [in Russian] Naukova Dumka, Kiev 1986.

    Google Scholar 

  11. Yu. E. Boyarintsev,Methods for Solving Singular Systems of Ordinary Differential Equations [in Russian] Nauka, Novosibirsk 1988.

    Google Scholar 

  12. A. B. Bakushinslii, “One method for the numerical solution of integral equations,”Zh. Vych. Mat. Mat. Fiz.,5, No. 4, 744–749 (1965).

    Google Scholar 

  13. V. V. Vasin and V. P. Tanana, “On stability of projective methods for solution of ill-posed problems,”Zh. Vych. Mat. Mat. Fiz.,15, No. 1, 19–29 (1975).

    MATH  MathSciNet  Google Scholar 

  14. W. Frair, “Continued fractions solutions to Fredholm integral equations,”Rocky Mountains J. Math.,4, No. 2, 357–360 (1974).

    Article  Google Scholar 

  15. M. S. Syavavko,Integral Continued Fractions [in Ukrainian] Naukova Dumka, Kiev 1994.

    MATH  Google Scholar 

  16. M. I. Rozhankivs’ka and M. S. Syavavko, “Operator continued fractions and construction of correct and stable methods for solution of three-diagonal systems of operator equations,”Dopov. Akad. Nauk Ukrainy, No. 9, 24–29 (1994).

    Google Scholar 

  17. M. S. Syavavko, T. V. Pasechnik, and O. M. Rybytska, “Pseudoinverse operator and rational algorithms for the normal solution of Fredholm integral equations of the first kind”Electron. Modelir.,17, No. 1, 10–16 (1995).

    Google Scholar 

  18. I. V. Sleshinskii, “On convergence of continued fractions,”Zap. Mat. Otd. Novoross. Obshch. Estestvoispyt.,8, 97–128 (1988).

    Google Scholar 

  19. V. Ya. Skorobogat’ko,Theory of Branching Continued Fractions and Its Application in Computational Mathematics [in Russian] Nauka, Moscow 1983.

    Google Scholar 

  20. D. I. Bodnar,Branching Continued Fractions [in Russian] Naukova Dumka, Kiev 1986.

    Google Scholar 

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Syavavko, M.S. J-fractional regularization of linear ill-posed equations. Ukr Math J 48, 1282–1298 (1996). https://doi.org/10.1007/BF02383874

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  • DOI: https://doi.org/10.1007/BF02383874

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