Algorithms for the computation of functionals defined on the solution of a discrete ill-posed problem |
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Authors: | Lars Eldén |
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Institution: | (1) Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden |
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Abstract: | We study a linear, discrete ill-posed problem, by which we mean a very ill-conditioned linear least squares problem. In particular we consider the case when one is primarily interested in computing a functional defined on the solution rather than the solution itself. In order to alleviate the ill-conditioning we require the norm of the solution to be smaller than a given constant. Thus we are lead to minimizing a linear functional subject to two quadratic constraints. We study existence and uniqueness for this problem and show that it is essentially equivalent to a least squares problem with a linear and a quadratic constraint, which is easier to handle computationally. Efficient algorithms are suggested for this problem. |
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Keywords: | 15A06 65F30 65K10 |
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