Correlated floating point errors

[Dean Schulze]

>...This is a key insight of many algorithms that
>obtain the benefit of higher precision without the cost, such as 
>"doubled double" quad.   This is not a bug in those algorithms, but an
>exploitation of an important feature of conventional floating-point 
>arithmetic: roundoff is NOT random. 

>...

>If I recall correctly, both Gaussian elimination and tridiagonal eigenvalue
>routines work better than they "should" because the errors in the
>intermediate results are correlated:  the answers come out fine even though
>the intermediate results may have no significant figures correct.


    I'd like to find out more about the use of correlated floating point
errors and how they are used in numerical algorithms. Can anyone provide
a reference?

	If the correaltion of floating point errors is due to round off I
wonder if these correlations are dependant on the rounding mode that is
used.  Is the performance of algorithms that depend upon these correlations
affected when the rounding mode is changed?

Dean Schulze