Geodesic
Max-min and min-max approximation problems for normal matrices revisited
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 159-166
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},
     year = {2014},
     volume = {41},
     zbl = {1296.90136},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a16/}
}
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AU  - Tichý,  Petr
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EP  - 166
VL  - 41
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%A Liesen,  Jörg
%A Tichý,  Petr
%T Max-min and min-max approximation problems for normal matrices revisited
%J Electronic transactions on numerical analysis
%D 2014
%P 159-166
%V 41
%U http://geodesic.mathdoc.fr/item/ETNA_2014__41__a16/
%G en
%F ETNA_2014__41__a16
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/