Minimization of Linear Functionals Defined on
Solutions of Large-Scale Discrete Ill-Posed Problems | Lars Elden, Per Christian Hansen, Marielba Rojas
| | 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. | | Keywords | Discrete ill-posed problems, confidence intervals, large-scale algorithms, trust regions. | | Type | Technical report | | Year | 2003 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Technical report-2003-25 | | Electronic version(s) | [ps] | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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