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annotate toolbox/pentoep.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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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function P = pentoep(n, a, b, c, d, e)
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Antonio Pino Robles <data.script93@gmail.com>
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2 %PENTOEP Pentadiagonal Toeplitz matrix (sparse).
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Antonio Pino Robles <data.script93@gmail.com>
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3 % P = PENTOEP(N, A, B, C, D, E) is the N-by-N pentadiagonal
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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4 % Toeplitz matrix with diagonals composed of the numbers
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Antonio Pino Robles <data.script93@gmail.com>
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5 % A =: P(3,1), B =: P(2,1), C =: P(1,1), D =: P(1,2), E =: P(1,3).
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Antonio Pino Robles <data.script93@gmail.com>
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6 % Default: (A,B,C,D,E) = (1,-10,0,10,1) (a matrix of Rutishauser).
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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7 % This matrix has eigenvalues lying approximately on
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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8 % the line segment 2*cos(2*t) + 20*i*sin(t).
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Antonio Pino Robles <data.script93@gmail.com>
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9 %
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Antonio Pino Robles <data.script93@gmail.com>
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10 % Interesting plots are
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11 % PS(FULL(PENTOEP(32,0,1,0,0,1/4))) - `triangle'
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Antonio Pino Robles <data.script93@gmail.com>
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12 % PS(FULL(PENTOEP(32,0,1/2,0,0,1))) - `propeller'
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Antonio Pino Robles <data.script93@gmail.com>
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13 % PS(FULL(PENTOEP(32,0,1/2,1,1,1))) - `fish'
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Antonio Pino Robles <data.script93@gmail.com>
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14
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15 % References:
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16 % R.M. Beam and R.F. Warming, The asymptotic spectra of
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17 % banded Toeplitz and quasi-Toeplitz matrices, SIAM J. Sci.
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18 % Comput. 14 (4), 1993, pp. 971-1006.
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19 % H. Rutishauser, On test matrices, Programmation en Mathematiques
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Antonio Pino Robles <data.script93@gmail.com>
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20 % Numeriques, Editions Centre Nat. Recherche Sci., Paris, 165,
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21 % 1966, pp. 349-365.
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22
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23 if nargin == 1, a = 1; b = -10; c = 0; d = 10; e = 1; end
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Antonio Pino Robles <data.script93@gmail.com>
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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25 P = spdiags([ a*ones(n,1) b*ones(n,1) c*ones(n,1) d*ones(n,1) ....
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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26 e*ones(n,1) ], -2:2, n, n);