On Thursday, March 20, 2014 5:32:15 PM UTC-4, Paweł Biernat wrote:
Taking into account your suggestions I came up with an ad-hoc
implementation tailored for my needs. Instead of computing
Laguerre(n,1,t-n) I compute the whole expression
Laguerre(n,1,t-n)*exp(-(t-n))*(t-n) via a function
W dniu piątek, 21 marca 2014 13:44:17 UTC+1 użytkownik Steven G. Johnson
napisał:
It would be better to avoid the NaNs in the first place (which come when
you multiply 0 * Inf, from an underflow times an overflow). For one thing,
floating-point exceptions are slow. For another thing,
On Thursday, March 20, 2014 8:26:56 AM UTC-4, Paweł Biernat wrote:
# implementation via recursive definition of laguerre polynomials
function laguerrel_recursive(n::Integer, alpha::Number, x::Number)
l0 = 1# L_{0}
l1 = 1+alpha-x# L_{1}
This
On Thursday, March 20, 2014 8:26:56 AM UTC-4, Paweł Biernat wrote:
So it seems that BigFloat is the major drawback. I really wander how
Mathematica handles the generation of Laguerre polynomials. I am aware of
the GSL bindings and the function sf_laguerre_n, but it also returns NaNs
for
For example, you may be able to use the analytical asymptotic form of the
Laguerre polynomial for large n. Computing special functions efficiently
is all about switching between different asymptotic forms, recurrences,
etcetera, for different regions of the parameter space.
Taking into account your suggestions I came up with an ad-hoc
implementation tailored for my needs. Instead of computing
Laguerre(n,1,t-n) I compute the whole expression
Laguerre(n,1,t-n)*exp(-(t-n))*(t-n) via a function laguerrel_xexpx.
Because I incorporated the exponential factor into the
