Paper Info
Title
A fast randomized Kaczmarz algorithm for sparse solutions of consistent linear systems
Abstract
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear equations with sparse solutions. The speedup is achieved by projecting every iterate onto a weighted row of the linear system while maintaining the random row selection criteria of Strohmer and Vershynin. The weights are chosen to attenuate the contribution of row elements that lie outside of the estimated support of the sparse solution. While the Kaczmarz algorithm and its variants can only find solutions to overdetermined linear systems, our algorithm surprisingly succeeds in finding sparse solutions to underdetermined linear systems as well. We present empirical studies which demonstrate the acceleration in convergence to the sparse solution using this modified approach in the overdetermined case. We also demonstrate the sparse recovery capabilities of our approach in the underdetermined case and compare the performance with that of $\ell_1$ minimization.
Year
Venue
Field
2013
CoRR
Overdetermined system,Mathematical optimization,Underdetermined system,Linear system,System of linear equations,Sparse approximation,Algorithm,Kaczmarz method,Algebraic Reconstruction Technique,Solver,Mathematics
DocType
Volume
Citations 
Journal
abs/1305.3803
5
PageRank 
References 
Authors
0.52
3
2
Name
Order
Citations
PageRank
Hassan Mansour134934.12
Özgür Yilmaz268551.36