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Asymptotics of the spectral norms of some interesting matrix sequences

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  • UserAlbrecht Böttcher (TU Chemnitz)
  • ClockFriday 26 February 2010, 15:00-16:00
  • HouseMR4, CMS.

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The talk concerns the asymptotic behavior of the spectral norm (which is the largest eigenvalue in the case of positive definite matrices) of the n-by-n truncations of infinite matrices as n goes to infinity. As examples, we consider matrices arising in the analysis time series with long memory and matrices that emerge in connection with best constants in inequalities of the Markov and Wirtinger types. The message of the talk is that a very fertile strategy for tackling the problem is an old idea by Harold Widom and Lawrence Shampine: replace matrices by integral operators and try to prove that the latter, after appropriate scaling, converge uniformly to a limiting integral operator.

This talk is part of the Applied and Computational Analysis series.

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