Minimization of functionals on the solution of a large-scale discrete ill-posed problem |
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Authors: | David R Martin Lothar Reichel |
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Institution: | 1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA
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Abstract: | In this work we study the minimization of a linear functional defined on a set of approximate solutions of a discrete ill-posed problem. The primary application of interest is the computation of confidence intervals for components of the solution of such a problem. We exploit the technique introduced by Eldén in 1990, utilizing a parametric programming reformulation involving the solution of a sequence of quadratically constrained least squares problems. Our iterative method, which uses the connection between Lanczos bidiagonalization and Gauss-type quadrature rules to bound certain matrix functionals, is well-suited for large-scale problems, and offers a significant reduction in matrix-vector product evaluations relative to available methods. |
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