Department of Mathematical Modelling

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An algorithm for computing piecewise constant solutions to fredholm integral equations

V.V. Tchernyi and A.V. Smirnova:

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Abstract

We describe an algorithm for computing the discontinuous solutions of Fredholm integral equations of the first kind, stable with respect to perturbation of the right-hand side of equation. The algorithm is based on regularizing CG iterations and consists of two steps: approximating the breakpoints of the exact solution and solving the original equation using the obtained breakpoints. If the right-hand side is perturbed, smoothing via iterative spline-approximation method is applied. The stability with respect to right-hand side perturbations is obtained via applying the residual criterion both for smoothing and to stop the CG iterations.

IMM Technical Report 9, 1997

Last modified June 4, 1997

For further information, please contact, Finn Kuno Christensen, IMM, Bldg. 321, DTU
Phone: (+45) 4588 1433. Fax: (+45) 4588 2673, E-mail: fkc@imm.dtu.dk

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