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annotate toolbox/grcar.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
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Antonio Pino Robles <data.script93@gmail.com>
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1 function G = grcar(n, k)
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2 %GRCAR Grcar matrix - a Toeplitz matrix with sensitive eigenvalues.
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Antonio Pino Robles <data.script93@gmail.com>
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3 % GRCAR(N, K) is an N-by-N matrix with -1s on the
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Antonio Pino Robles <data.script93@gmail.com>
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4 % subdiagonal, 1s on the diagonal, and K superdiagonals of 1s.
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Antonio Pino Robles <data.script93@gmail.com>
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5 % The default is K = 3. The eigenvalues of this matrix form an
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Antonio Pino Robles <data.script93@gmail.com>
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6 % interesting pattern in the complex plane (try PS(GRCAR(32))).
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8 % References:
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9 % J.F. Grcar, Operator coefficient methods for linear equations,
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10 % Report SAND89-8691, Sandia National Laboratories, Albuquerque,
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11 % New Mexico, 1989 (Appendix 2).
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12 % N.M. Nachtigal, L. Reichel and L.N. Trefethen, A hybrid GMRES
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13 % algorithm for nonsymmetric linear systems, SIAM J. Matrix Anal.
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14 % Appl., 13 (1992), pp. 796-825.
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16 if nargin == 1, k = 3; end
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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18 G = tril(triu(ones(n)), k) - diag(ones(n-1,1), -1);