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Block Kaczmarz Method with Inequalities

The Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equalities. This paper studies a system of linear equalities and inequalities. We use the block version of the Kaczmarz method applied towards the equalities with the simple randomized Kaczmarz scheme for the inequalities. This primarily involves combining Needell and Tropp's work on the block Kaczmarz method with the application of a randomized Kaczmarz approach towards a system of equalities and inequalities performed by Leventhal and Lewis. We give an expected linear rate of convergence for this kind of system and find that using the block Kaczmarz scheme for the equalities can improve the rate compared to the simple Kaczmarz method.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cmc_theses-1954
Date01 January 2014
CreatorsBriskman, Jonathan
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceCMC Senior Theses
Rights© 2014 Jonathan Briskman

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