Block Kaczmarz Method with Inequalities

Authors

Jonathan Briskman
Deanna Needell, Claremont McKenna CollegeFollow

Document Type

Article - preprint

Department

Mathematics (CMC)

Publication Date

6-28-2014

Abstract

The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell and Tropp provided an analysis of a block version of the method for systems of linear equations. This paper considers the use of a block type method for systems of mixed equalities and inequalities, bridging these two bodies of work. We show that utilizing a matrix paving over the equalities of the system can lead to significantly improved convergence, and prove a linear convergence rate as in the standard block method. We also demonstrate that using blocks of inequalities offers similar improvement only when the system satisfies a certain geometric property. We support the theoretical analysis with several experimental results.

Comments

Featured in Journal of Mathematical Imaging and Vision, vol. 52, num. 3, 385–396, 2015.

Rights Information

© 2014 Briskman, Needell

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Briskman, J., Needell, D., "Block Kaczmarz Method with Inequalities", arXiv preprint arXiv:1406.7339, 2014.