Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS

John W. Hilgers, Barbara S. Bertram and William R. Reynolds

Chapter 16 in Integral Methods in Science and Engineering, 2002, pp 105-110 from Springer

Abstract: Abstract Solving first kind Fredholm integral equations with Hilbert-Schmidt kernels and the standard L 2-topology is well known to be difficult because the problem is ill-posed, meaning the inverse operator, or generalized inverse operator if the former does not exist, is unbounded. The practical consequence of this is that any linear system that models the integral equation is necessarily ill-conditioned, usually to the point where direct attempts to solve the system by conventional methods produce nothing, or solutions that are useless due to extreme instabilities.

Keywords: True Solution; Tikhonov Regularization; Regularization Operator; Small Minimum; Brute Force Search (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0111-3_16

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DOI: 10.1007/978-1-4612-0111-3_16

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