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On one approach to the discretization of the lavrent’ev method

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Abstract

We propose a new scheme of discretization of the Lavrent’ev method for operator equations of the first kind with self-adjoint nonnegative operators of certain “smoothness.” This scheme is more economical in the sense of the amount of used discrete information as compared with traditional approaches.

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References

  1. G. M. Vainikko and A. Yu. Veretennikov, Iteration Procedures in Ill-Posed Problems [in Russian], Nauka, Moscow 1986.

    Google Scholar 

  2. V. V. Vasin, “Discrete convergence and finite-dimensional approximation of regularizing algorithms,” Zh. Vych. Mat. Mat. Fiz., 19, No. 1, 11–21 (1979).

    MATH  MathSciNet  Google Scholar 

  3. R. Plato and G. Vainikko, “On the regularization of the Rietz-Galerkin method for solving ill-posed problems,” Uchen. Zap. Tart. Univer., 863, 3–17 (1989).

    MathSciNet  Google Scholar 

  4. R. Plato and G. Vainikko, “On the regularization of projection methods for solving ill-posed problems,” Numer. Math., 57, 63–70 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  5. S. G. Solodkii, “Optimization of adaptive direct methods for the solution of operator equations in a Hilbert space,” Ukr Mat. Zh., 42, No. 1, 95–102 (1990).

    Article  MathSciNet  Google Scholar 

  6. S. G. Krein (editor), Functional Analysis [in Russian], Nauka, Moscow 1972.

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Authors
  1. S. V. Pereverzev
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  2. S. G. Solodkii
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Pereverzev, S.V., Solodkii, S.G. On one approach to the discretization of the lavrent’ev method. Ukr Math J 48, 239–247 (1996). https://doi.org/10.1007/BF02372049

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  • DOI: https://doi.org/10.1007/BF02372049

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