Minimization of Linear Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems |
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| Authors: | L. Eldén P. C. Hansen M. Rojas |
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| Affiliation: | (1) Department of Mathematics, Link?ping University, Link?ping, S-581 83, Sweden;(2) Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, Kgs. Lyngby, DK-2800, Denmark;(3) Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, USA |
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| Abstract: | The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Eldén proposed an algorithm for this minimization problem based on a parametric programming reformulation involving the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat conduction problem. AMS subject classification (2000) 65F22 |
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| Keywords: | discrete ill-posed problems confidence intervals large-scale algorithms trust regions |
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