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Calcolo
Published in: Calcolo 4/2017

07-04-2017

Partial condition number for the equality constrained linear least squares problem

Authors: Hanyu Li, Shaoxin Wang

Published in: Calcolo | Issue 4/2017

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Abstract

In this paper, the normwise condition number of a linear function of the equality constrained linear least squares solution called the partial condition number is considered. Its expression and closed formulae are first presented when the data space and the solution space are measured by the weighted Frobenius norm and the Euclidean norm, respectively. Then, we investigate the corresponding structured partial condition number when the problem is structured. To estimate these condition numbers with high reliability, the probabilistic spectral norm estimator and the small-sample statistical condition estimation method are applied and two algorithms are devised. The obtained results are illustrated by numerical examples.
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Metadata
Title
Partial condition number for the equality constrained linear least squares problem
Authors
Hanyu Li
Shaoxin Wang
Publication date
07-04-2017
Publisher
Springer Milan
Published in
Calcolo / Issue 4/2017
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-017-0221-8

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