On Sat, 2003-12-06 at 14:18, Brian Hurt wrote:
> 30 decimal digits is enough accuracy to measure the 
> distance between here and the Andromeda Galaxy in microns.  Why does he 
> need such a ridiculous amount of precision?

Standard eigen problem sometimes needs ridiculous precision:
the scalar product of two vectors:

	sigma (i=1,n) (v1_i * v2_i)

sometimes involves cancellation of large values.
To see why there is a problem here, consider:

	1.000001e20 - 1e20 -
	(1.000001e-20 - 1e-20) 

and you can see you need around 50 digits precision, just to get
an answer with 1 digit of precision.

The eigen problem with large numbers of dimensions
arises in, for example, quantum chemistry. 

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