Article: An iterative method for solving Fredholm integral equations of the first kind Journal: International Journal of Computing Science and Mathematics (IJCSM) 2009 Vol.2 No.4 pp.354 - 379 Abstract: The purpose of this paper is to give a convergence analysis of the iterative scheme: uδn = quδn−1 + (1 − q)T−1an K* fδ, uδ0 = 0, where T := K*K, Ta := T + aI, q ∈ (0, 1), an := α0qn, α0 > 0, with finite-dimensional approximations of T and K* for solving stably Fredholm integral equations of the first kind with noisy data. Inderscience Publishers - linking academia, business and industry through research

Title: An iterative method for solving Fredholm integral equations of the first kind

Authors: Sapto W. Indratno, A.G. Ramm

Addresses: Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA. ' Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA

Abstract: The purpose of this paper is to give a convergence analysis of the iterative scheme: uδn = quδn−1 + (1 − q)T−1a_n K* f_δ, uδ₀ = 0, where T := K*K, Ta := T + aI, q ∈ (0, 1), an := α0qⁿ, α0 > 0, with finite-dimensional approximations of T and K* for solving stably Fredholm integral equations of the first kind with noisy data.

Keywords: FIEFK; Fredholm integral equations of the first kind; iterative regularisation; variational regularisation; discrepancy principle; DSM; dynamical systems method; noisy data.

DOI: 10.1504/IJCSM.2009.030913

International Journal of Computing Science and Mathematics, 2009 Vol.2 No.4, pp.354 - 379

Published online: 11 Jan 2010 *

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Title: An iterative method for solving Fredholm integral equations of the first kind

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