DOI: https://doi.org/10.26089/NumMet.v16r101

An error estimate of a regularizing algorithm based on the generalized residual principle when solving integral equations

Authors

  • V.P. Tanana
  • A.I. Sidikova

Keywords:

regularization
generalized residual method
modulus of continuity
error estimates
ill-posed problems
integral equations
operator equations
finite-dimensional approximations

Abstract

A regularizing algorithm for the approximate solution of integral equations of the first kind is studied. This algorithm involves a finite-dimensional approximation of the original problem. An error estimate is proposed. In order to obtain this estimate, the equivalence of the generalized residual method and the generalized residual principle is proved. This result can be used to estimate the finite-dimensional approximations of regularized solutions.

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Published

2015-01-19

Issue

Vol. 16 (2015): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

V.P. Tanana

South Ural State University
• Professor

A.I. Sidikova

South Ural State University
• Associate Professor

References

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