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Pseudospectra of a Spectral Approximation of the First Derivative
Dimension N=17

This figure illustrates approximate pseudospectra of the first derivative operator d/dx on [-1,1] with boundary condition u(1)=0. The pseudospectra of the infinite dimensional operator consist of half-planes. This is suggested in this low-dimensional discretization by the straight lines that form the rightmost part of each pseudospectral boundary. For more information, see [Tre92].

Use the following MATLAB code compute a similar image using EigTool.

  [D,x] = cheb(18);       % cheb.m from Trefethen's "Spectral Methods in MATLAB"
  A = D(2:end,2:end);
  opts.npts=50; = [-60 10 -35 35];
  opts.levels = -6:0;
Download this code: specdiff.m.
Download cheb.m from L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.