The Mathematical Institute, University of Oxford, Eprints Archive

Wave packet pseudomodes of twisted Toeplitz matrices

Trefethen, L. N. and Chapman, S. J. (2004) Wave packet pseudomodes of twisted Toeplitz matrices. Communications in Pure and Applied Mathematics, 57 (9). pp. 1233-1264. ISSN 0010-3640

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Abstract

The pseudospectra of banded, 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, related to Hörmander's commutator condition for partial differential equations, -pseudoeigenvectors of such matrices for exponentially small values of exist in the form of localized wave packets. The symbol need not be smooth with respect to x, just differentiable at a point (or less).

Item Type:Article
Subjects:D - G > Difference and functional equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:296
Deposited By:Jon Chapman
Deposited On:03 Oct 2006
Last Modified:20 Jul 2009 14:20

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