| Popis: |
The choice of basis functions for a given mathematical expansion is critical. It determines whether the expansion is uniformly convergent, whether the expansion can be differentiated termwise, and finally whether this differentiated expansion is uniformly convergent. Basis functions that are chosen with these considerations in mind also provide much faster convergence, and sometimes more meaningful extrapolation, than do those chosen simply on the basis of mean square convergence. These points must be kept in mind when comparing regional models, such as rectangular harmonic and spherical cap harmonic models, whose basis functions have been chosen to give different expansion properties. |
