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annotate toolbox/wilk.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.
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1 function [A, b] = wilk(n)
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2 %WILK Various specific matrices devised/discussed by Wilkinson.
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3 % [A, b] = WILK(N) is the matrix or system of order N.
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4 % N = 3: upper triangular system Ux=b illustrating inaccurate solution.
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5 % N = 4: lower triangular system Lx=b, ill-conditioned.
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6 % N = 5: HILB(6)(1:5,2:6)*1.8144. Symmetric positive definite.
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7 % N = 21: W21+, tridiagonal. Eigenvalue problem.
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8
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9 % References:
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10 % J.H. Wilkinson, Error analysis of direct methods of matrix inversion,
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11 % J. Assoc. Comput. Mach., 8 (1961), pp. 281-330.
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12 % J.H. Wilkinson, Rounding Errors in Algebraic Processes, Notes on Applied
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13 % Science No. 32, Her Majesty's Stationery Office, London, 1963.
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14 % J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University
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15 % Press, 1965.
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16
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17 if n == 3
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18 % Wilkinson (1961) p.323.
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19 A = [ 1e-10 .9 -.4
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20 0 .9 -.4
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21 0 0 1e-10];
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22 b = [ 0 0 1]';
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23
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24 elseif n == 4
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25 % Wilkinson (1963) p.105.
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26 A = [0.9143e-4 0 0 0
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27 0.8762 0.7156e-4 0 0
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28 0.7943 0.8143 0.9504e-4 0
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29 0.8017 0.6123 0.7165 0.7123e-4];
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30 b = [0.6524 0.3127 0.4186 0.7853]';
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31
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32 elseif n == 5
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33 % Wilkinson (1965), p.234.
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34 A = hilb(6);
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35 A = A(1:5, 2:6)*1.8144;
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36
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37 elseif n == 21
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38 % Taken from gallery.m. Wilkinson (1965), p.308.
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39 E = diag(ones(n-1,1),1);
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40 m = (n-1)/2;
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41 A = diag(abs(-m:m)) + E + E';
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42
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43 else
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44 error('Sorry, that value of N is not available.')
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45 end