[Rd] make check on DU4 with R-1.1.0 snapshot

[Prof Brian D Ripley]

On 2 Jun 2000, Peter Dalgaard BSA wrote:

> Albrecht Gebhardt <albrecht.gebhardt@uni-klu.ac.at> writes:
> 
> > > abs(X - s$u %*% D %*% t(s$v)) - Eps
> >               [,1]          [,2]
> > [1,] -2.109424e-15 -2.220446e-16
> > [2,] -1.998401e-15 -8.881784e-16
> > [3,] -2.220446e-15 -1.776357e-15
> > [4,] -1.998401e-15 -1.332268e-15
> > [5,] -1.998401e-15 -1.332268e-15
> > [6,] -1.998401e-15  4.440892e-16
> > [7,] -1.332268e-15 -2.220446e-15
> > > abs(D - t(s$u) %*% X %*% s$v) - Eps
> >               [,1]          [,2]
> > [1,]  3.108624e-15 -8.881784e-16
> > [2,] -1.165734e-15 -2.220446e-15
> > 
> > 4.440892e-16 and 3.108624e-15 
> > 
> > Eps was: 
> > > Eps
> > [1] 2.220446e-15
> ...
> >  eps:  2.22044605E-16
> 
> So one of the calculations end up at about 5.3e-15 which is over 20
> times the machine epsilon. OK, Hilbert matrices are nasty and AFAIR
> Alpha hardware doesn't have the extended precision of Intel FPUs but
> does this look reasonable enough that we should just use a bigger Eps?

Other hardware with standard IEEE arithmetic succeeds. But I think
Eps = 100 * .Machine$double.eps would be adequate.  My Solaris box gets up
to 1.77e-15.  I've just committed 100 * .Machine$double.eps.

Brian

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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