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comparison toolbox/grcar.m @ 0:8f23314345f4 draft

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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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1 function G = grcar(n, k)
2 %GRCAR Grcar matrix - a Toeplitz matrix with sensitive eigenvalues.
3 % GRCAR(N, K) is an N-by-N matrix with -1s on the
4 % subdiagonal, 1s on the diagonal, and K superdiagonals of 1s.
5 % The default is K = 3. The eigenvalues of this matrix form an
6 % interesting pattern in the complex plane (try PS(GRCAR(32))).
7
8 % References:
9 % J.F. Grcar, Operator coefficient methods for linear equations,
10 % Report SAND89-8691, Sandia National Laboratories, Albuquerque,
11 % New Mexico, 1989 (Appendix 2).
12 % N.M. Nachtigal, L. Reichel and L.N. Trefethen, A hybrid GMRES
13 % algorithm for nonsymmetric linear systems, SIAM J. Matrix Anal.
14 % Appl., 13 (1992), pp. 796-825.
15
16 if nargin == 1, k = 3; end
17
18 G = tril(triu(ones(n)), k) - diag(ones(n-1,1), -1);