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comparison toolbox/smoke.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
parents 8f23314345f4
children
comparison
equal deleted inserted replaced
1:e471a92d17be 2:c124219d7bfa
1 function A = smoke(n, k)
2 %SMOKE Smoke matrix - complex, with a `smoke ring' pseudospectrum.
3 % SMOKE(N) is an N-by-N matrix with 1s on the
4 % superdiagonal, 1 in the (N,1) position, and powers of
5 % roots of unity along the diagonal.
6 % SMOKE(N, 1) is the same except for a zero (N,1) element.
7 % The eigenvalues of SMOKE(N, 1) are the N'th roots of unity;
8 % those of SMOKE(N) are the N'th roots of unity times 2^(1/N).
9 %
10 % Try PS(SMOKE(32)). For SMOKE(N, 1) the pseudospectrum looks
11 % like a sausage folded back on itself.
12 % GERSH(SMOKE(N, 1)) is interesting.
13
14 % Reference:
15 % L. Reichel and L.N. Trefethen, Eigenvalues and pseudo-eigenvalues of
16 % Toeplitz matrices, Linear Algebra and Appl., 162-164:153-185, 1992.
17
18 if nargin < 2, k = 0; end
19
20 w = exp(2*pi*i/n);
21 A = diag( [w.^(1:n-1) 1] ) + diag(ones(n-1,1),1);
22 if k == 0, A(n,1) = 1; end