How to generate a badly conditioned matrix?

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Beaya
Beaya 2013-11-9
编辑： Matt J 2013-11-9
I want to test how, badly conditioning of a matrix A, will affect calculation of A*x = b where A is my increasingly badly conditioned matrix and x is a vector of ones, so we know the exact solution. This is my code, however it gives me correct results no matter how badly conditioned my matrix is. Do you have any suggestions on what am I doing wrong?
n = 31;
for a = 1:n-1;
A = gallery('randsvd',a,a,4);
%disp(A)
x = ones(a,1);
b = A*x;
xGauss=A\b
xInv=inv(A)*b
end

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回答（1 个）

Matt J
Matt J 2013-11-9
编辑：Matt J 2013-11-9
I don't think you've actually checked cond(A). Your matrices aren't all that ill-conditioned, for any a=1...30. Here's an example where you can see the effects of ill-conditioning
for a = 1:n-1;
A=vander(1:a);
x = ones(a,1);
b = A*x;
errorSlash=norm(A\b-1)
errorInv=norm(inv(A)*b-1)
end

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