TY - RPRT

T1 - Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems

AU - Elden, Lars

AU - Hansen, Per Christian

AU - Rojas, Marielba

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - trust regions.

KW - large-scale algorithms

KW - Discrete ill-posed problems

KW - confidence intervals

M3 - Report

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

ER -