We can consider Equation (10) as a Taylor series expansion, therefore we can write it
in a more compact, but equivalent, form as
| |
(11) |
This equation describes the local Born-Fourier a.k.a. pseudo-screen method
Huang and Wu (1996).
The extended local Born-Fourier method, Equation (10), is preferable in practice, since
Equation (11) can lead to instability when the denominator vanishes. Another way of
avoiding the instability is to add a small complex quantity, , to the
denominator, method that is known as the complexified local Born-Fourier or
complexified pseudo-screen method de Hoop and Wu (1996):
| |
(12) |