I am reading Honkai Zhao's original paper on the fast sweeping algorithm.
I am looking at equation 2.6:
https://graphics.stanford.edu/courses/cs468-03-fall/Papers/zhao_fastsweep1.pdf
I am trying to understand what that is actually saying.
Like if I were to write an algorithm to actually compute $\bar x$ what do I actually have to do?
Additionally, I am trying to understand how this is related to the original problem of solving the eikonal equation. Basically why does that series of polynomials express an approximaiton to the original equation?