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From: HengTong DING on 29 Oct 2009 09:45

> Sight... the value 1.827500000000000e+02 alone is *meaningless* to judge the accuracy.

Yes, sure.

183 of what unit? If it's 183 unit-weight of an electron it's negligible compared to the weight of an elephant.
>
that's exaggerative, the ratio of the mass of an elephant to an electron is about 10^34.
Anyway, it will be ok. THanks for your prompt reply!
>> norm(KWK)

ans =

3.239472531925387e+15

>> norm(KWK - KWK')

ans =

1.828107974111172e+02
From: dpb on 29 Oct 2009 09:59
HengTong DING wrote:
....
> Thanks for your information. As the matrix W here is a symmetric
> matrix, balance() does not help. In my specific problem the ratio of the
> largest diagonal entry to the smallest one is the order of 10^12, which
> may explain the ill-conditioned singular values. BUT here I do not do
> the inversion of W and just do SVD, so it does not matter whether W is
> ill-conditioned or not.

....

Well, since there are only about 15 decimal digits of precision in
double precision, that means there are only about 3 digits of precision
in the smallest value as compared to the largest. This is the root
cause of your problems and clearly it _does_ make a difference in SVD as
well as in inversion...

I don't know about a specific implementation for higher precision, sorry.

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