QuoteOriginally posted by: outrunQuoteOriginally posted by: CuchulainnThe (1,1) Pade approximation to exp(-z) is about 5 times faster. I tried it in a binomial tree pricer. Did not look at it since a while but continued fractions might be your friend.Nice. That would giveexp(z) = which is indeed very compact.. but what is the precision?This is O(z^2) by taking the series expansion of R(1,1) and comparing to exp(z). Higher order Pade R(m,n) give even better accuracy.BTW R(1,1) aka Cayley transform for Schroedinger's PDE.You would need to examine the radius of convergence to check for which values of z .. but it's all documented in the literature. Maybe used a swith depending on the value of z; if in a radius use Pade, otherwise exp(z)? In many apps z will be like exp(-r*deltaT)..Pade appoximants are very important in ODEU_t + AU = 0sol U(t) = exp(-At).Then R(1,1) == Crank NiclsonR(1,0) and R(0.1) == Euler twinsDo Microsoft /Intel use Pade, or is it something else? I think it is worth having a look at these approximations.
Last edited by Cuchulainn
on October 10th, 2010, 10:00 pm, edited 1 time in total.