Talk:Reciprocal difference

Why?
Why is this concept of reciprocal difference important? Why is it defined the way that it is rather than some other way? JRSpriggs 05:11, 17 February 2007 (UTC)

Alternative expressions?
The expression of reciprocal difference on the current revision of the main page seems excessive and ornate.

Perhaps it should be expressed more simply?

Perhaps, something like:


 * $$\rho_{-1} = 0$$


 * $$\rho_0(x) = f(x)$$


 * $$\rho_n(x_0, x_1, ..., x_n)= \frac{x_0 - x_n}{\rho_{n-1}(x_0, ..., x_n-1) - \rho_{n-1}(x_1, ..., x_n)} + \rho_{n-2}(x_1, ..., x_{n-1})$$

...but we really need better notation for this:

Here, the subscript on $$\rho$$ is one less than the length of the argument list, here. And, thus, that subscript does not carry any information but should be a useful aid to understanding. But in my opinion it just winds up being confusing in this case.

Furthermore, the mechanism of describing lists by describing their elements suffers when dealing with inductive cases which lead down to empty lists.

But the entry on Thiele's_interpolation_formula depends on this definition so I do not feel comfortable changing the conventions of notation.

Rdmil (talk) 17:46, 13 October 2010 (UTC)