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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Persian Gulf University, Bushehr, Iran

    Saeed Karimi & Meisam Jozi

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  1. Saeed Karimi
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  2. Meisam Jozi
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Correspondence to Saeed Karimi.

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Communicated by M. Hadizadeh.

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Karimi, S., Jozi, M. Weighted Conjugate Gradient-Type Methods for Solving Quadrature Discretization of Fredholm Integral Equations of the First Kind. Bull. Iran. Math. Soc. 45, 455–473 (2019). https://doi.org/10.1007/s41980-018-0143-5

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  • DOI: https://doi.org/10.1007/s41980-018-0143-5

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