I was going through the 2005 paper on "Smile interpolation and calibration of the local volatility model" by Nabil Kahale (attached). He gives Algorithm A which he describes as in attachment 1. The c(j) and gamma(j) are mentioned in Theorem 3 of the same paper as in attachment 2.
Unfortunately I am stuck at step 2, not knowing how to initiate these values for the loop. Can someone, who has probably tried this method earlier, help me?
Thanks a lot!