Tensorial Model for Photolithography Aerial Image Simulation

Algorithm 2

Fixed-point

(1) Choose 𝐾, the number of principal axes or eigenvectors required to estimate. Consider matrix 𝐓 and set

   𝑝←1.

(2) Initialize eigenvector 𝐮_𝑝 of size 𝑑×1, for example, randomly;

(3) Update 𝐮_𝑝 as 𝐮_𝑝←𝐓𝐮_𝑝;

(4) Do the Gram-Schmidt orthogonalization process 𝐮_𝑝←𝐮_𝑝−∑^{𝑗=𝑝−1}_𝑗=1(𝐮^𝑇_𝑝𝐮_𝑗)𝐮_𝑗;

(5) Normalize 𝐮_𝑝 by dividing it by its norm: 𝐮_𝑝←𝐮_𝑝/‖𝐮_𝑝‖.

(6) If 𝐮_𝑝 has not converged, go back to step 3.

(7) Increment counter 𝑝←𝑝+1 and go to step 2 until 𝑝 equals 𝐾.