# Basic PageRank algorithm

I am trying to understand the pageRank algorithm by reading the original article:

http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf

I have some issues understanding the algorithm at paragraph 2.6 . I try to report it here. This reads:

$$R_0 \leftarrow S$$

loop:

$$R_{i+1} \leftarrow AR_i$$

$$d \leftarrow ||R_{i}||_1-||R_{i+1}||_1$$

$$R_{i+1} \leftarrow R_{i+1}+dE$$

$$\delta \leftarrow ||R_{i+1}-R_i ||_1$$

while $$\epsilon > \delta$$

where:

• $$S$$ is almost any initial starting vector $$\in R^k$$, $$k>1$$ ;

• $$E$$ is a fixed vector belonging to $$R^k$$, $$A$$ is a fixed matrix of dimensions $$k x k$$ ;

• || ||_1 is the $$L^1$$ norm ;

• $$\epsilon$$ is a scalar number for convergence ;

From the article I understand that with this algorithm $$R_i$$ should converge to the largest eigenvalue of $$A+E \times 1^+$$ where $$1$$ is the vector of all ones, but I do not see why. Further, they say that the "$$d$$ factor maintains $$||R||_1$$" but I do not see why and in which sense.

MY TRIAL:

For $$E=0$$, this looks like the power method to find the largest eigenvalue of A. But there is no normalization so I do not understand why $$||R||_1$$ is "maintened" ?