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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 2, pp 455–473 | Cite as

Weighted Conjugate Gradient-Type Methods for Solving Quadrature Discretization of Fredholm Integral Equations of the First Kind

  • Saeed KarimiEmail author
  • Meisam Jozi
Original Paper
  • 29 Downloads

Abstract

A variant of conjugate gradient-type methods, called weighted conjugate gradient (WCG), is given to solve quadrature discretization of various first-kind Fredholm integral equations with continuous kernels. The WCG-type methods use a new inner product instead of the Euclidean one arising from discretization of \(L^2\)-inner product by the quadrature formula. On this basis, the proposed algorithms generate a sequence of vectors which are approximations of solution at the quadrature points. Numerical experiments on a few model problems are used to illustrate the performance of the new methods compared to the CG-type methods.

Keywords

Ill-posed problem First-kind integral equation Quadrature discretization Iterative method CG-type methods 

Mathematics Subject Classification

Primary 45A05 Secondary 45Q05 45N05 45P05 65F22 65F10 

Notes

Acknowledgements

The authors would like to thank Prof. Andreas Kleefeld for his MATLAB code for discretization of a first-kind integral equations on a surface by boundary element method.

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsPersian Gulf UniversityBushehrIran

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