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annotate toolbox/dorr.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 [c, d, e] = dorr(n, theta)
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2 %DORR Dorr matrix - diagonally dominant, ill conditioned, tridiagonal.
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3 % [C, D, E] = DORR(N, THETA) returns the vectors defining a row diagonally
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4 % dominant, tridiagonal M-matrix that is ill conditioned for small
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5 % values of the parameter THETA >= 0.
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6 % If only one output parameter is supplied then
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7 % C = FULL(TRIDIAG(C,D,E)), i.e., the matrix iself is returned.
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8 % The columns of INV(C) vary greatly in norm. THETA defaults to 0.01.
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9 % The amount of diagonal dominance is given by (ignoring rounding errors):
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10 % COMP(C)*ONES(N,1) = THETA*(N+1)^2 * [1 0 0 ... 0 1]'.
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11
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12 % Reference:
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13 % F.W. Dorr, An example of ill-conditioning in the numerical
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14 % solution of singular perturbation problems, Math. Comp., 25 (1971),
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15 % pp. 271-283.
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16
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17 if nargin < 2, theta = 0.01; end
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18
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19 c = zeros(n,1); e = c; d = c;
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20 % All length n for convenience. Make c, e of length n-1 later.
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21
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22 h = 1/(n+1);
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23 m = floor( (n+1)/2 );
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24 term = theta/h^2;
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25
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26 i = (1:m)';
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27 c(i) = -term*ones(m,1);
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28 e(i) = c(i) - (0.5-i*h)/h;
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29 d(i) = -(c(i) + e(i));
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30
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31 i = (m+1:n)';
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32 e(i) = -term*ones(n-m,1);
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33 c(i) = e(i) + (0.5-i*h)/h;
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34 d(i) = -(c(i) + e(i));
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35
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36 c = c(2:n);
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37 e = e(1:n-1);
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38
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39 if nargout <= 1
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40 c = tridiag(c, d, e);
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41 end