Matlab-condition number of a matrix

evi
2013 11 23
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更新时间：2013 11 24
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Using matlab,I found that the condition number of matrix A(using the infinity norm,Koo(A)) (where A is is the Hilbert matrix with dimension n=200 ) is 3.8586e+020
Is this right or am I wrong?

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John D'Errico
John D'Errico 2013-11-23

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No. It is probably a bigger number than that However, you forget the limits of floating point arithmetic.

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evi
evi 2013-11-23
How can I find the right number for the condition number of the matrix???
evi
evi 2013-11-23
编辑：evi 2013-11-24
Or do you mean that I can't find the exact number,using matlab??
evi
evi 2013-11-24
When I run my code,I get this warning message: Matrix is close to singular or badly scaled.Results may be inaccurate.RCOND:2.591645e-021.What does this mean?
John D'Errico
John D'Errico 2013-11-24
The "true" condition number? The that value will be difficult to compute using doubles. You would need to work symbolically, and even that will take some serious effort. For example, if you converted a matrix of doubles to syms, they are already in error because the doubles are only floating point approximations to the numbers in your matrix. So knowing the exact condition number is only something one could do by building the matrix as a symbolic one directly. I suppose you could use my HPF toolbox to work with high precision floating point numbers, but I've never written an SVD tool for HPF.
John D'Errico
John D'Errico 2013-11-24
编辑：John D'Errico 2013-11-24
MATLAB is telling you that your matrix is numerically singular. (READ THE MESSAGE! It did say the matrix is close to singular.) A numerically singular matrix is one that cannot be distinguished from a singular matrix when floating point arithmetic is employed.
evi
evi 2013-11-24
Nice...Thank you...!
John D'Errico
John D'Errico 2013-11-24
As a followup, I decided to add a few linear algebra tools to HPF. So far this am, chol, LU, det were easy and now done. svd will take longer.

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evi
evi 2013-11-24

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I have also an other question.If we have the tridiagonal matrix,that has the number 4 at the main diagonal and the number 1 at the first diagonal below the main diagonal and at the first diagonal above the main diagonal,I get that the condition number,using the infinity norm,is 3,independent from the dimension I give..Is this right???If yes,why does this happen??Why isn't there any change of the condition number??

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John D'Errico
John D'Errico 2013-11-24
编辑：John D'Errico 2013-11-24
If you want to ask a separate question, then ask it as another question, not as an answer to your first question. When you ask it like this, you cause confusion, and make it difficult for others to follow.

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