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Wave packet pseudomodes of twisted Toeplitz matrices

By L. N. Trefethen and S. J. Chapman

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)

Topics: Difference and functional equations
Year: 2004
DOI identifier: 10.1002/cpa.20034
OAI identifier: oai:generic.eprints.org:296/core69

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