On Tue, 2007-02-06 at 19:32 -0500, Stavros Macrakis wrote:
> Since floor uses bfloat internally, this seems like a very roundabout,
> computationally expensive, and potentially incorrect way of
> calculating the continued fraction of a power. It would be much more
> straightforward and computationally efficient (though possibly just as
> likely to be incorrect) to do cf(bfloat(...)),fpprec:xxx with some
> sort of loop increasing the fpprec as needed. And that would work for
> *arbitrary* expressions, not just a^b.
If I understand the algorithms being discussed here, a rational
approximation to an expression is computed to some provided precision
and then the (finite) continued fraction of that rational is computed.
My question is at what point in the sequence of terms of the finite CF
does the sequence start to diverge from the sequence of terms of the
exact (infinite) CF? Is there any useful relationship between the
precision of the rational approximation and the number of correct terms
in the approximating CF?
There are methods for generating the terms of the CFs for some algebraic
irrationals (in addition to quadratic surds) one at a time; how do such
methods compare with the algorithms discussed here?
-- Bill Wood