Geodesic
Max-min and min-max approximation problems for normal matrices revisited
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 159-166.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give a new proof of an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory, and constrained convex optimization. Our proof uses a classical characterization theorem from approximation theory and thus exploits the link between the two approximation problems with normal matrices on the one hand and approximation problems on compact sets in the complex plane on the other.
Classification : 41A10, 30E10, 49K35, 65F10
Keywords: matrix approximation problems, MIN-MAX and MAX-MIN approximation problems, best approximation, normal matrices 
@article{ETNA_2014__41__a16,
     author = {Liesen, J\"org and Tich\'y, Petr},
     title = {Max-min and min-max approximation problems for normal matrices revisited},
     journal = {Electronic transactions on numerical analysis},
     pages = {159--166},
     publisher = {mathdoc},
     volume = {41},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a16/}
}
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Liesen, Jörg; Tichý, Petr. Max-min and min-max approximation problems for normal matrices revisited. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 159-166. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a16/