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 wit...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 299; no. Suppl 1; pp. 217 - 224
Main Authors Tanana, V. P., Sidikova, A. I.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2017
Springer Nature B.V
Subjects
Algorithms
Discretization
Integral equations
Mathematics
Mathematics and Statistics
Regularization
error estimate
ill-posed problem
regularization
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543817090231