[Help-gsl] gsl_sum (potential division by zero?)

[Michel Van den Bergh]

Hi,

I am not a numerical analyst (IANANA) but it seems to me that even in
levin_utrunc.c no motivation
is given for discarding zero terms.

The division by zero problem occurs because in the levin_u transform if
some terms f(n)  in
a series are zero, so are the corresponding remainder estimates nf(n).
But it seems to me that
division by zero can also occur deeper in the algorithm.

Wouldn't it be more natural to add a bit of noise to the remainder
estimates to reduce the risk
of division by zero? It seems to me that adding a bit of noise to the
remainder
estimates would not fundamentally alter the convergence properties of
the levin_u transform.
The remainder estimates are very crude anyway.

But again IANANA.

Regards,
Michel