  We theoretically investigate spin-wave dispersion in rare-earth magnet
compounds by using first-principles calculations and a method we call the
reciprocal-space algorithm (RSA). The value of the calculated exchange
stiffness for Nd$_2$Fe$_{14}$B is within the range of reported experimental
values. We find that the exchange stiffness is considerably anisotropic when
only short-range exchange couplings are considered, whereas inclusion of
long-range couplings weakens the anisotropy. In contrast, $R$Fe$_{11}$Ti
($R$=Y, Nd, Sm) shows large anisotropy in the exchange stiffness.
