# Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank

arXiv: https://arxiv.org/abs/1508.07607 · HTML: https://mlsanity.com/paper/1508.07607/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2015.

## Built on by (most cited first, 3 of 3)

- [Large-Scale Sequential Learning for Recommender and Engineering Systems](https://mlsanity.com/paper/2205.06893/) (2022)
- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)
- [Accelerated Evolving Set Processes for Local PageRank Computation](https://mlsanity.com/paper/2510.08010/) (2025)

## Abstract (arXiv)

In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first algorithm is based on the gradient descent in L1 norm instead of the Euclidean one. The second algorithm extends the Frank-Wolfe to support sparse gradient updates. The third algorithm stands for the mirror descent algorithm with a randomized projection. We proof converges rates for these methods for sparse problems as well as numerical experiments support their effectiveness.