Weighted Conjugate Gradient-Type Methods for Solving Quadrature Discretization of Fredholm Integral Equations of the First Kind
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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.
KeywordsIll-posed problem First-kind integral equation Quadrature discretization Iterative method CG-type methods
Mathematics Subject ClassificationPrimary 45A05 Secondary 45Q05 45N05 45P05 65F22 65F10
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.
- 7.Dold, A., Eckmann, B.: Iterative methods for the solution of a linear operator equation in Hilbert space. Springer-Verlag, New York (1974)Google Scholar
- 25.Saad, Y.: Iterative methods for sparse linear systems. University of Minnesota, Minneapolis (2000)Google Scholar