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Projection methods for the solution of Fredholm integral equations of the first kind with (ϕ, β)-differentiable kernels and random errors

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Abstract

We estimate errors of projection methods for the solution of the Fredholm equaitons of the first kindAx=y+ζ with random perturbation ζ under the assumption that the integral operatorA has a (ϕ, β)-differentiable kernel and the mathematical expectation of ∥ξ∥2 does not exceed σ2. Under these assumptions, we obtain an estimate that is a complete analog of the well-known result by Vainikko and Plato for the deterministic case where ∥ξ∥≤σ.

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References

  1. A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    MATH  Google Scholar 

  2. R. Plato and G. Vainikko, “On regularization of projection methods for solving ill-posed problems,”Numer. Math.,57, 63–79 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  3. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan,Probabilistic Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

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  4. A. V. Bakushinskii, “On the construction of regularizing algorithms under random interferences,”Dokl. Akad. Nauk SSSR,189, No. 2, 231–233 (1969).

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  5. A. M. Fedotov,Ill-Posed Problems with Random Errors in Initial Data [in Russian], Nauka, Novosibirks (1990).

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Authors
  1. G. A. Pereverzeva
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 713–717, May, 1999.

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Pereverzeva, G.A. Projection methods for the solution of Fredholm integral equations of the first kind with (ϕ, β)-differentiable kernels and random errors. Ukr Math J 51, 793–798 (1999). https://doi.org/10.1007/BF02591713

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  • DOI: https://doi.org/10.1007/BF02591713

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