How to make a nxm Vandermonde matrix?

Question

Johanne 2019-9-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/481181-how-to-make-a-nxm-vandermonde-matrix

编辑： John D'Errico 2019-9-19

采纳的回答： John D'Errico

How to make a mxn Vandermonde matrix?

n = 30;

start = -2;

stop = 2;

x = linspace(start,stop,n);

eps = 1;

rng(1);

r = rand(1,n) * eps;

y = x.*(cos(r+0.5*x.^3)+sin(0.5*x.^3));

%plot(x,y,'o');

m = 3;

B = y';

b = B(1:m);

A = fliplr(vander(x(1:m)))

This makes it a 3x3 matrix, and I want a nx3 matrix.

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Answer 1

John D'Errico 2019-9-19

1
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https://ww2.mathworks.cn/matlabcentral/answers/481181-how-to-make-a-nxm-vandermonde-matrix#answer_392638

编辑：John D'Errico 2019-9-19

在 MATLAB Online 中打开

A = x(:).^(2:-1:0);

That works as long as you are using MATLAB R2016b or later. Earlier releases would need to use bsxfun, or even repmat.

Note that in A, i used the convention that vander uses, having the higest order term first. This is somewhat standard in MATLAB, for example, with polyfit.

You used fliplr on the result of vander, so you have the constant term first in your example. Either way is acceptable, as long as you know what you are doing.