You can use pagemtimes to perform both multiplications but, since chol accept only matrices (2D arrays) as arguments, you'll still need a loop. Try the code below:
n = size(Pf, 3);
aux = pagemtimes(Fn, Pf);
aux = pagemtimes(aux, Fn');
for i = 1:n
aux (:,:,i) = chol(aux(:,:,i));
end
aux = pagemtimes(aux, rand(3,1,n));
If you desire retrieve the steps taken, you may avoid overwriting the aux variable renaming the sucessive results as aux1, aux2 etc, or other names of your preference.
