Toeplitz Matrices with Slowly Growing Pseudospectra

Albrecht Böttcher () and Sergei Grudsky ()
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Albrecht Böttcher: TU Chemnitz, Faculty of Mathematics
Sergei Grudsky: Rostov on Don State University, Faculty of Mechanics and Mathematics

A chapter in Factorization, Singular Operators and Related Problems, 2003, pp 43-54 from Springer

Abstract: Abstract Let T(a) be the infinite Toeplitz matrix with the symbol a and let T n (a) denote the n × n principal submatrix of T(a). The pseudospectra of T n (a) are known to converge to the pseudospectrum of T(a) as n → ∞ provided a is piecewise continuous. Only recently, Mark Embree, Nick Trefethen, and one of the authors observed that this convergence may be spectacularly slow in case a has a jump. The main result of this paper says that such a slow convergence of pseudospectra is generic even within the class of continuous symbols.

Keywords: Toeplitz matrix; Toeplitz determinant; pseudospectrum. (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0227-0_4

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DOI: 10.1007/978-94-017-0227-0_4

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