Mercurial > matrix-functions
view toolbox/chebvand.m @ 2:c124219d7bfa draft
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 |
line wrap: on
line source
function C = chebvand(m,p) %CHEBVAND Vandermonde-like matrix for the Chebyshev polynomials. % C = CHEBVAND(P), where P is a vector, produces the (primal) % Chebyshev Vandermonde matrix based on the points P, % i.e., C(i,j) = T_{i-1}(P(j)), where T_{i-1} is the Chebyshev % polynomial of degree i-1. % CHEBVAND(M,P) is a rectangular version of 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. if nargin == 1, p = m; end n = max(size(p)); % Handle scalar p. if n == 1 n = p; p = seqa(0,1,n); end if nargin == 1, m = n; end p = p(:).'; % Ensure p is a row vector. C = ones(m,n); 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