[Bug-gsl] [bug #40092] false position root finding requires too many function evals

[Max]

Follow-up Comment #5, bug #40092 (project gsl):

The quick fix may be to check that x_linear differs
from x_left and x_right by some value. Some multiple of
GSL_DBL_EPSILON since required precision is not available
by design.

I do not think that additional tests of function values
may help since the derivative of the function can
be arbitrary large or small close to the root: 1e9*(x - 1)
or 1e-9*(x - 1).

> 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.

That is why I tried to raise discussion on gsl-help
instead of reporting a bug.

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