On Estimating the Error of an Approximate Solution Caused by the Discretization of an Integral Equation of the First Kind

Abstract

We study a regularization algorithm for the approximate solution of integral equations of the first kind. This algorithm includes a finite-dimensional approximation of the problem. More exactly, the integral equation is discretized in two variables. An error estimate of the algorithm is obtained with the use of the equivalence of the generalized discrepancy method and the generalized discrepancy principle.

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Correspondence to V. P. Tanana.

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Original Russian Text © V.P. Tanana, A.I. Sidikova, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 1.

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Tanana, V.P., Sidikova, A.I. On Estimating the Error of an Approximate Solution Caused by the Discretization of an Integral Equation of the First Kind. Proc. Steklov Inst. Math. 299, 217–224 (2017). https://doi.org/10.1134/S0081543817090231

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Keywords

  • regularization
  • error estimate
  • ill-posed problem.