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annotate toolbox/chebvand.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
parents 8f23314345f4
children
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Antonio Pino Robles <data.script93@gmail.com>
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1 function C = chebvand(m,p)
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2 %CHEBVAND Vandermonde-like matrix for the Chebyshev polynomials.
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3 % C = CHEBVAND(P), where P is a vector, produces the (primal)
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4 % Chebyshev Vandermonde matrix based on the points P,
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5 % i.e., C(i,j) = T_{i-1}(P(j)), where T_{i-1} is the Chebyshev
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6 % polynomial of degree i-1.
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7 % CHEBVAND(M,P) is a rectangular version of CHEBVAND(P) with M rows.
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8 % Special case: If P is a scalar then P equally spaced points on
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9 % [0,1] are used.
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11 % Reference:
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12 % N.J. Higham, Stability analysis of algorithms for solving confluent
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13 % Vandermonde-like systems, SIAM J. Matrix Anal. Appl., 11 (1990),
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14 % pp. 23-41.
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16 if nargin == 1, p = m; end
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17 n = max(size(p));
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19 % Handle scalar p.
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20 if n == 1
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21 n = p;
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22 p = seqa(0,1,n);
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23 end
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25 if nargin == 1, m = n; end
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27 p = p(:).'; % Ensure p is a row vector.
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28 C = ones(m,n);
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29 if m == 1, return, end
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30 C(2,:) = p;
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31 % Use Chebyshev polynomial recurrence.
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32 for i=3:m
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33 C(i,:) = 2.*p.*C(i-1,:) - C(i-2,:);
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34 end