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The Matrix Computation Toolbox

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The Matrix Computation Toolbox


Nick Higham


11 Sep 2002 (Updated )

A collection of M-files for carrying out various numerical linear algebra tasks.

vand(m, p)
function V = vand(m, p)
%VAND   Vandermonde matrix.
%       V = VAND(P), where P is a vector, produces the (primal)
%       Vandermonde matrix based on the points P, i.e. V(i,j) = P(j)^(i-1).
%       VAND(M,P) is a rectangular version of VAND(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, Accuracy and Stability of Numerical Algorithms,
%       Second edition, Society for Industrial and Applied Mathematics,
%       Philadelphia, PA, 2002; chap. 22.

if nargin == 1, p = m; end
n = length(p);

%  Handle scalar p.
if n == 1
   n = p;
   p = linspace(0,1,n);

if nargin == 1, m = n; end

p = p(:).';                    % Ensure p is a row vector.
V = ones(m,n);
for i=2:m
    V(i,:) = p.*V(i-1,:);

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