Name
Title | ||
|---|---|---|
Convergence Rates for Greedy Kaczmarz Algorithms, and Faster Randomized Kaczmarz Rules Using the Orthogonality Graph. |
Abstract | ||
|---|---|---|
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a non-asymptotic convergence rate analysis for this algorithm, spurring numerous extensions and generalizations of the Kaczmarz method. Rather than the randomized selection rule analyzed in that work, in this paper we instead discuss greedy and approximate greedy selection rules. We show that in some applications the computational costs of greedy and random selection are comparable, and that in many cases greedy selection rules give faster convergence rates than random selection rules. Further, we give the first multi-step analysis of Kaczmarz methods for a particular greedy rule, and propose a provably-faster randomized selection rule for matrices with many pairwise-orthogonal rows. |
Year | Venue | Field |
|---|---|---|
2016 | UAI'16 Proceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence | Convergence (routing),Mathematical optimization,Iterative method,Generalization,Computer science,Algorithm,Orthogonality,Greedy algorithm,Kaczmarz method,Rate of convergence,Greedy randomized adaptive search procedure |
DocType | Volume | ISSN |
Journal | abs/1612.07838 | Conference on Uncertainty in Artificial Intelligence 2016 |
ISBN | Citations | PageRank |
978-0-9966431-1-5 | 0 | 0.34 |
References | Authors | |
0 | 6 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. Nutini | 1 | 83 | 4.10 |
| Behrooz Sepehry | 2 | 0 | 0.34 |
| Issam H. Laradji | 3 | 79 | 9.40 |
| Mark W. Schmidt | 4 | 1295 | 84.47 |
| Hoyt A. Koepke | 5 | 41 | 3.74 |
| Alim Virani | 6 | 21 | 1.59 |