A Finite Algorithm for the Minimum $l_\infty $ Solution to a System of Consistent Linear Equations

A column exchange algorithm is presented for the determination of a minimum $l_\infty $ solution to a system of consistent linear equations. The algorithm is based on first solving the associated dual problem as specified by a well-known theorem from functional analysis and then generating the requi...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1973-09, Vol.10 (4), p.607-617
Main Author: Cadzow, James A.
Format: Article
Language:English
Subjects:
Algorithms
Control theory
Linear equations
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Summary:A column exchange algorithm is presented for the determination of a minimum $l_\infty $ solution to a system of consistent linear equations. The algorithm is based on first solving the associated dual problem as specified by a well-known theorem from functional analysis and then generating the required solution by means of an alignment criterion. The procedure has been shown to have a rapid speed of convergence on all examples treated to date.
ISSN:0036-1429
1095-7170
DOI:10.1137/0710053