The Mathematical Institute, University of Oxford, Eprints Archive

Wave packet pseudomodes of twisted Toeplitz matrices

Trefethen, Lloyd N. and Chapman, S. J. (2002) Wave packet pseudomodes of twisted Toeplitz matrices. Technical Report. Unspecified. (Submitted)

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Abstract

The pseudospectra of nonsymmetric Toeplitz or circulant matrices with varying coefficients are considered. Such matrices are characterized by a symbol that depends on both position (x) and wave number (k). It is shown that when a certain winding number or twist condition is satisfied, analogous to Hörmander's commutator condition for partial differential equations, \varepsilon-pseudoeigenvectors of such matrices for exponentially small values of \varepsilon exist in the form of localized wave packets. The symbol need not be smooth, just differentiable at a point (or less).

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1206
Deposited By:Lotti Ekert
Deposited On:19 May 2011 07:40
Last Modified:19 May 2011 07:40

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