Selectable Set Randomized Kaczmarz
Abstract
The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz is a variant of RK that leverages existing information about the Kaczmarz iterate to identify an adaptive “selectable set” and thus yields an improved convergence guarantee. In this article, we propose a general perspective for selectable set approaches and prove a convergence result for that framework. In addition, we define two specific selectable set sampling strategies that have competitive convergence guarantees to those of other variants of RK. One selectable set sampling strategy leverages information about the previous iterate, while the other leverages the orthogonality structure of the problem via the Gramian matrix. We complement our theoretical results with numerical experiments that compare our proposed rules with those existing in the literature.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 30, 2022
- Source ID
- 10.1002/nla.2458
Entities
People
- Daji Landis
- Deanna Needell
- Jacob D. Moorman
- Thomas K. Tu
- William Swartworth
- Yotam Yaniv
Organizations
- Defense Advanced Research Projects Agency
- National Science Foundation
- University of California