Follow-up Comment #4, bug #40092 (project gsl):
Thank you for your further input.
As you say, the real problem is that the current design is not ideal because
it does not make the desired precision available to the iteration routine.
And this can result in more iterations than are necessary.
It appears that the residual test is intended to handle this situation but
this also involves an extra function evaluation on each iteration because the
solvers don't return function values.
This clearly needs fixing but it requires design changes that will break
backwards compatibility so we have unfortunately had to put this off to GSL
version 2.x.
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