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author Antonio Pino Robles <data.script93@gmail.com>
date Fri, 29 May 2015 09:48:36 +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 A = gfpp(T, c)
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2 %GFPP Matrix giving maximal growth factor for Gaussian elim. with pivoting.
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Antonio Pino Robles <data.script93@gmail.com>
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3 % GFPP(T) is a matrix of order N for which Gaussian elimination
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4 % with partial pivoting yields a growth factor 2^(N-1).
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5 % T is an arbitrary nonsingular upper triangular matrix of order N-1.
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6 % GFPP(T, C) sets all the multipliers to C (0 <= C <= 1)
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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7 % and gives growth factor (1+C)^(N-1).
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8 % GFPP(N, C) (a special case) is the same as GFPP(EYE(N-1), C) and
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9 % generates the well-known example of Wilkinson.
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10
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11 % Reference:
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12 % N.J. Higham and D.J. Higham, Large growth factors in
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13 % Gaussian elimination with pivoting, SIAM J. Matrix Analysis and
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14 % Appl., 10 (1989), pp. 155-164.
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15
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16 if norm(T-triu(T),1) | any(~diag(T))
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17 error('First argument must be a nonsingular upper triangular matrix.')
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18 end
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19
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20 if nargin == 1, c = 1; end
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21
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22 if c < 0 | c > 1
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23 error('Second parameter must be a scalar between 0 and 1 inclusive.')
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24 end
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25
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26 [m, m] = size(T);
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27 if m == 1 % Handle the special case T = scalar
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28 n = T;
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29 m = n-1;
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30 T = eye(n-1);
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31 else
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32 n = m+1;
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33 end
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34
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35 d = 1+c;
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36 L = eye(n) - c*tril(ones(n), -1);
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37 U = [T (d.^[0:n-2])'; zeros(1,m) d^(n-1)];
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38 A = L*U;
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39 theta = max(abs(A(:)));
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40 A(:,n) = (theta/norm(A(:,n),inf)) * A(:,n);