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Minimization of Linear Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems

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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.

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, Linköping, S-581 83, Sweden

    L. Eldén

  2. Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, Kgs. Lyngby, DK-2800, Denmark

    P. C. Hansen

  3. Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC, 27109, USA

    M. Rojas

Authors
  1. L. Eldén
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  2. P. C. Hansen
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  3. M. Rojas
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Corresponding authors

Correspondence to L. Eldén, P. C. Hansen or M. Rojas.

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AMS subject classification (2000)

65F22

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Eldén, L., Hansen, P. & Rojas, M. Minimization of Linear Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems. Bit Numer Math 45, 329–340 (2005). https://doi.org/10.1007/s10543-005-7122-y

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