Re: Where a generalized Richardson extrapolation routine would fit in GSL?

[Rhys Ulerich <rhys dot ulerich at gmail dot com>]

Thanks for looking through the patch Brian.

> One question: it looks like this
> extrapolates a vector quantity.  For simplicity, would it make sense
> to work with scalars as in the gsl_sum routines -- since presumably
> that is the common case -- or is there some application where vector
> extrapolation is unavoidable? (could each component can be
> extrapolated independently?)

You're right that each component could be extrapolated independently.
I wrote it using vectors because doing so allows using BLAS calls for
the linear algebra and speeds up many component use cases.  I'd prefer
to keep the code vector-capable under the covers under the theory that
people extrapolating only a scalar at a time aren't all that worried
about speed.

My vector use case arose from testing convergence orders for
timesteppers (non-GSL, but similar in interface) that manipulate
vectors of state variables.

If you'd like, I can submit an additional patch that 1) Renames
gsl_extrap_richardson to something like gsl_extrap_richardson_vector,
2) Provides  a scalar-only gsl_extrap_richardson that wraps up scalars
and calls the gsl_extrap_richardson_vector routines under the covers,
and 3) Exercises the scalar-only wrappers fully in the test suite.
That way if someone later does need a faster scalar-only version, he
or she can change over the underlying implementation without fear of
regression.

- Rhys