# Horner's scheme for sine Tailor's series computatioin stability

1. Sep 24, 2006

### Touchkin

1. Why is the standard Horner's scheme for the computation of Taylor's series for sine unstabil?
The standard scheme is sin(x) = x(1 + x^2(-1/3! + x^2(1/5! + x^2(-1/7! + ... x^2(-1/(2n-1)! + x^2/(2n+1)!)...)

2. How can we modify the scheme to make it stabil?

I think instability is somehow connected with the changing sign of the terms in the Taylor's series, but I am not sure how. If you have any ideas ar you know the answer it will be interesting to hear.