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Weighted conjugate gradient-type methods for solving quadrature discretization of Fredholm integral equations of the first kind. (English) Zbl 1411.65166

Summary: 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.

MSC:

65R20 Numerical methods for integral equations
45A05 Linear integral equations
45B05 Fredholm integral equations
45Q05 Inverse problems for integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
45P05 Integral operators
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F10 Iterative numerical methods for linear systems

Software:

LSQR; GKB-FP; LSMR; CRAIG
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Full Text: DOI

References:

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