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ShfitedPowGMRES
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Methods for solving PageRank with multiple damping factors
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Luca Lombardo 36b5da4bca Changed norm 1 with norm 2. This does not change the fact that the shifted-GMRES doesn't work 2 years ago
testing Changed norm 1 with norm 2. This does not change the fact that the shifted-GMRES doesn't work 2 years ago
tex added plor of mv in function of alpha 2 years ago
.gitattributes clear stats 2 years ago
.gitignore small fixes 2 years ago
README.md final version 2 years ago
algo.py Changed norm 1 with norm 2. This does not change the fact that the shifted-GMRES doesn't work 2 years ago
main.py now the program prints the number of mv for each iteration in the standard power method 2 years ago
requirements.txt small fixes 2 years ago

README.md

Documentation

Report of the project: view / download

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