Volume 41, pp. 159-166, 2014.

Max-min and min-max approximation problems for normal matrices revisited

Jörg Liesen and Petr Tichý


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.

Full Text (PDF) [113 KB]

Key words

matrix approximation problems, min-max and max-min approximation problems, best approximation, normal matrices

AMS subject classifications

41A10, 30E10, 49K35, 65F10

Links to the cited ETNA articles

[1]Vol. 33 (2008-2009), pp. 17-30 M. Bellalij, Y. Saad, and H. Sadok: Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization
[6]Vol. 12 (2001), pp. 205-215 Bernd Fischer and Franz Peherstorfer: Chebyshev approximation via polynomial mappings and the convergence behaviour of Krylov subspace methods

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