Corpus ID: 17165019

Preconditioning in Expectation

@article{Cohen2014PreconditioningIE,
  title={Preconditioning in Expectation},
  author={Michael B. Cohen and Rasmus Kyng and Jakub W. Pachocki and Richard Peng and Anup B. Rao},
  journal={ArXiv},
  year={2014},
  volume={abs/1401.6236}
}
We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the nearly-optimal ones given by [Kolla-Makarychev-Saberi-Teng STOC`10]. Combining this with the recursive preconditioning framework by [Spielman-Teng STOC`04] and improved embedding algorithms, this leads to algorithms that solve symmetric diagonally dominant… Expand
Solving SDD linear systems in nearly mlog1/2n time
Efficient Õ(n/∊) Spectral Sketches for the Laplacian and its Pseudoinverse
Efficient $\widetilde{O}(n/\epsilon)$ Spectral Sketches for the Laplacian and its Pseudoinverse
A Spectral Approach to the Shortest Path Problem
Essays on Banking Competition
Faster Least Squares Optimization

References

SHOWING 1-10 OF 36 REFERENCES
A Note on Preconditioning by Low-Stretch Spanning Trees
Spectral Sparsification of Graphs
A Nearly-m log n Time Solver for SDD Linear Systems
A Matrix Hyperbolic Cosine Algorithm and Applications
...
1
2
3
4
...