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function C = chebvand(m, p, classname) %CHEBVAND Vandermonde-like matrix for the Chebyshev polynomials. % C = GALLERY('CHEBVAND',P), where P is a vector, produces the % (primal) Chebyshev Vandermonde matrix based on the points P: % C(i,j) = T_{i-1}(P(j)), where T_{i-1} is the Chebyshev % polynomial of degree i-1. % GALLERY('CHEBVAND',M,P) is a rectangular version of % GALLERY('CHEBVAND',P) with M rows. % Special case: If P is a scalar, then P equally spaced points on % [0,1] are used. % Reference: % N. J. Higham, Stability analysis of algorithms for solving confluent % Vandermonde-like systems, SIAM J. Matrix Anal. Appl., 11 (1990), % pp. 23-41. % % Nicholas J. Higham % Copyright 1984-2005 The MathWorks, Inc. if isempty(p), p = m; square = 1; else square = 0; end n = length(p); % Handle scalar p. if n == 1 n = p; p = linspace(zeros(classname),1,n); end if square == 1, m = n; end p = p(:).'; % Ensure p is a row vector. C = ones(m,n,classname); if m == 1, return, end C(2,:) = p; % Use Chebyshev polynomial recurrence. for i=3:m C(i,:) = 2.*p.*C(i-1,:) - C(i-2,:); end