numerical errors in eigen decomp

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Harish Guruprasad 2011-4-12

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Hi, I have computed a matrix, which (If it was done right) i know to be Positive semi definite. I did a eigen decomposition using eig and got the following result

min(eig(m2))

ans =

-9.8601e-14

A sample of the other eigen values is below -0.0000, -0.0000, -0.0000, 0.0000, 0.0000, 0.0000, 1.0047, 4.6499, 10.6999, 33.8846, 38.4610, 46.6943, 49.3577, 51.3520, 156.0164, 217.2181, 315.0000

Is it safe to assume the negative eigen values are through numerical issues and not due to a problem in the matrix computation?

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Answer 1

the cyclist 2011-4-12

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Yes. "eig" was probably about the first MATLAB function ever written, decades ago, so I think you will find it reliable. :-)

A value of e-14 is about the numerical error you would expect in a double-precision calculation of this type.

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Andrew Newell 2011-4-12

In addition, judging by the spread of eigenvalues, your matrix is ill-conditioned. That would contribute to the error.

Matt Tearle 2011-4-12

Yep. Largest evalue is 10^2, smallest is 10^-13. That's as much accuracy as you can expect from double precision arithmetic. I'd call that good and move on.

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