Deriving convergence state

[cieske]

Hi! Thanks for the great work. There are two convergence states in eq.9 and eq.16 in your paper, may I ask the process of deriving \beta{u,i} and \omega{i,j}?

[kyriemao]

Hi! Thanks for the great work. There are two convergence states in eq.9 and eq.16 in your paper, may I ask the process of deriving \beta{u,i} and \omega{i,j}?

Hi cieske,

For eq.9, it is derived from eq.8 by transposing the "\frac{1}{d_u + 1} e_u" in the right side to the left side, and you can get "\frac{d_u}{d_u + 1} e_u = ...e_i". Then multiply "\frac{d_u + 1}{d_u}" to the both sides, and you can get eq.9.

For eq.16, its derivation is the same as eq.9. You can first write an equation like eq.8 as "ei = \frac{G{i, i}}{g_i} ei + \frac{G{i, k}}{\sqrt{g_i}\sqrt{g_k}} e_k". Then you will get eq.16.

[cieske]

I understand. Thank you for your reply!