Efficient numerical method of the fiber Bragg grating synthesis
  A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance. 
O.V. Belai, L.L. Frumin, E.V. Podivilov, D.A. Shapiro