I think I have a typo in equation 17.3.8 (The Bulirsch-Stoer Method). When I try to evaluate it for (k=1, j=0), a perfectly valid combination, I get a zero divide as (k-j = k) when j = 0. Looking at the code for the implementation in WebNote 21, I think the denominator in 17.3.8 should read:

[(n sub k / n sub j)^2] - 1

Anyway, thanks for the book!

Hi Richard,

There is indeed a typo in this equation: the subscript k-j in the denominator should be k-j-1.

Decoding the implementation in WebNote 21 is a little tricky: the T's are in reverse order in each row and each T is just one row, not the whole matrix in eqn. 17.3.8. (The second index in the code is for the vector of y's).

Thanks for catching this.
Saul Teukolsky

Hi Saul, thanks for getting back to me! Thanks also for the clarification on interpreting the code. You're right, I didn't notice the fact that the coefficients get read back in the reverse order. I've spent the intervening time going over the code to make sure I understand it.