Re: RFC: Differential Arithmetic Library

From: deane_yang (Deane_Yang_at_[hidden])
Date: 2002-02-13 20:54:55

--- In boost_at_y..., Peter Schmitteckert (boost) <boost_at_s...> wrote:
> Dear Martin,
> My plans are:
> 1) implement a taylor series with respect to one variable
> 2) implement differentiation with respect to >1 variables.
> 
> Best wishes
> Peter

Peter,

Do you mean higher order Taylor series for 1 variable,
but just first order in several variables? This makes
sense to me, although you might be able to implement
second order Taylor series in several variables using
a good symmetric matrix class.

As for how to compute the exponential of a higher order
Taylor series, the formula in several variables is EASIER
to derive than the single variable formula. Of course, the
latter follows easily from the former. It comes down to
computing higher order partial derivatives of f(g(x)),
and then setting f = exp. This works fine for exp, sin, cos,
log, since their higher order derivatives are easy to compute.
Functions like tan and atan look pretty hard to me.

Deane