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Galerkin information, the hyperbolic cross, and the complexity of operator equations

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Abstract

We obtain an exact power order of the complexity of the approximate solution of a certain class of operator equations in a Hibert space. We show that the optimal power order is realized by an algorithm that uses Galerkin information associated with the hyperbolic cross. As a corollary we derive an exact power order of the complexity of the approximate solution of Volterra integral equations whose kernels and free terms belong to Sobolev classes.

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev

    S. V. Pereverzev & K. Sh. Makhkamov

Authors
  1. S. V. Pereverzev
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  2. K. Sh. Makhkamov
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 639–648, May, 1991.

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Pereverzev, S.V., Makhkamov, K.S. Galerkin information, the hyperbolic cross, and the complexity of operator equations. Ukr Math J 43, 593–601 (1991). https://doi.org/10.1007/BF01058546

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  • DOI: https://doi.org/10.1007/BF01058546

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