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

Lars Elden, Per Christian Hansen, Marielba Rojas

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    Abstract

    The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden 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.
    Original languageEnglish
    PublisherInformatics and Mathematical Modelling, Technical University of Denmark, DTU
    Publication statusPublished - 2003

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