The Mathematical Institute, University of Oxford, Eprints Archive

Piecewise continuous Toeplitz matrices and operators: slow approach to infinity

Boettcher, A. and Embree, Mark and Trefethen, Lloyd N. (2000) Piecewise continuous Toeplitz matrices and operators: slow approach to infinity. Technical Report. Unspecified. (Submitted)

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Abstract

The pseudospectra of banded finite dimensional Toeplitz matrices rapidly converge to the pseudospectra of the corresponding infinite dimensional operator. This exponential convergence makes a compelling case for analyzing pseudospectra of such Toeplitz matrices, not just eigenvalues. But what if the matrix is dense and its symbol has a jump discontinuity? The pseudospectra of the finite matrices still converge, but it is shown here that the rate is no longer exponential in the matrix dimension, only algebraic.

The second and third authors were supported by UK Engineering and Physical Sciences Research Council Grant GR/M12414.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Linear and multilinear algebra; matrix theory
O - Z > Operator theory
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1254
Deposited By:Lotti Ekert
Deposited On:21 May 2011 17:06
Last Modified:21 May 2011 17:06

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