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Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. I

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Abstract

We construct a new system of discretization of the Fredholm integral equations of the first kind with linear compact operators A and free terms from the set Range (A(A*A)V), v > 1/2. The approach proposed enables one to obtain the optimal order of error on such classes of equations by using a considerably smaller amount of discrete information as compared with standard schemes.

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Authors and Affiliations

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

    S. G. Solodkii

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  1. S. G. Solodkii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 699–711, May, 1998.

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Solodkii, S.G. Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. I. Ukr Math J 50, 795–808 (1998). https://doi.org/10.1007/BF02514332

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  • DOI: https://doi.org/10.1007/BF02514332

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