On Estimating the Error of an Approximate Solution Caused by the Discretization of an Integral Equation of the First Kind
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.
Keywordsregularization error estimate ill-posed problem.
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- 5.V. P. Tanana and A. I. Sidikova, “An error estimate for a regularizing algorithm based on the generalized discrepancy principle in the solution of integral equations,” Zh. Vychisl. Met. Programmir. 16 (1), 1–9 (2015).Google Scholar
- 6.V. P. Tanana, “On an iterative projection algorithm for first-order operator equations with perturbed operator,” Dokl. AN SSSR 224 (15), 1025–1029 (1975).Google Scholar