This repository contains the code of my attempt to replicate the results obtained in `[1]`

. The scripts are all written in python and are heavily build around the libraries SciPy and NumPy. To install all the required packages with `pip`

run the following command in terminal

`pip install -r requirements.txt`

At the moment, the standard and shifted power method to compute the PageRank with multiple damping factors are fully implemented (as described in `[1]`

). To run the program we need to execute the `main.py`

file. It takes as input two arguments:

`--dataset`

: the options are`BerkStan`

and`Stanford`

. This commands selects the web-graph to run the algorithms on.`--algo`

: the options are`power`

,`shifted`

,`both`

. If you choose the last option, it will first run the standard power method and then the shifted one.

Here an example of what’s described above.

`./main.py --dataset Stanford --algo both`

## Under development

In the `testing/`

folder there are two python notebook that contains the attempt on replicating the results obtained in `[1]`

for the shifted GMRES method. The implementation of the Arnoldi process is fully working. On the other hand, there are several problems on the shifted GMRES algorithm that I can’t figure out.

## References

`[1]`

*Zhao-Li Shen, Meng Su, Bruno Carpentieri, and Chun Wen. Shifted power-gmres method accelerated by extrapolation for solving pagerank with multiple damping factors. Applied Mathematics and Computation, 420:126799, 2022*