Extrapolation procedures
The Ranking of Nodes in Networks

According to Theorem 1, r_c is a rational function with a numerator of degree p – 1 with vector coefficients and a scalar denominator of degree p – 1. Moreover, r_c tends to the PageRank vector $\overline{r}$ when c tends to 1.

We'll therefore calculate r_c for various values of c smaller than the desired one (we've already mentioned that the extra cost is low thanks to properties 7 and 8), interpolate these vectors by a rational fraction of the same type but with smaller degrees, and then extrapolate this rational fraction to the desired point c. Of course, for such a procedure to provide good results, it is necessary that the extrapolating rational fraction represents the...