{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/157014"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/157014","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Effects of Data Heterogeneity on Distributed Linear System Solvers","abstract":"We focus on the fundamental problem of solving a system of linear equations. In particular, we are interested in distributed linear system solvers, where one taskmaster coordinates any number of workers to attain a solution. There are two predominant and fundamentally different ways of doing this: optimization-based and projection-based solvers. Although there is extensive literature on both classes of algorithms, a rigorous analytical comparison of their performance is lacking. Consequently, there is no concrete understanding of why numerical experiments show that projection-based solvers tend to perform better in many real and synthetic scenarios. In this work, we develop a framework for such analysis, and we use that framework to investigate the comparison of optimization-based and projection-based solvers.","abstract_html":"We focus on the fundamental problem of solving a system of linear equations. In particular, we are interested in distributed linear system solvers, where one taskmaster coordinates any number of workers to attain a solution. There are two predominant and fundamentally different ways of doing this: optimization-based and projection-based solvers. Although there is extensive literature on both classes of algorithms, a rigorous analytical comparison of their performance is lacking. Consequently, there is no concrete understanding of why numerical experiments show that projection-based solvers tend to perform better in many real and synthetic scenarios. In this work, we develop a framework for such analysis, and we use that framework to investigate the comparison of optimization-based and projection-based solvers.","abstract_has_math":false,"creators":["Velasevic, Boris"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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In particular, we are interested in distributed linear system solvers, where one taskmaster coordinates any number of workers to attain a solution. There are two predominant and fundamentally different ways of doing this: optimization-based and projection-based solvers. Although there is extensive literature on both classes of algorithms, a rigorous analytical comparison of their performance is lacking. Consequently, there is no concrete understanding of why numerical experiments show that projection-based solvers tend to perform better in many real and synthetic scenarios. In this work, we develop a framework for such analysis, and we use that framework to investigate the comparison of optimization-based and projection-based solvers."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Effects of Data Heterogeneity on Distributed Linear System Solvers"]}]}],"canonical_facts":{"dc:contributor.advisor":["Azizan, Navid"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Velasevic, Boris"],"dc:date.accessioned":["2024-09-24T18:26:48Z"],"dc:date.available":["2024-09-24T18:26:48Z"],"dc:date.issued":["2024-05"],"dc:description.abstract":["We focus on the fundamental problem of solving a system of linear equations. In particular, we are interested in distributed linear system solvers, where one taskmaster coordinates any number of workers to attain a solution. There are two predominant and fundamentally different ways of doing this: optimization-based and projection-based solvers. Although there is extensive literature on both classes of algorithms, a rigorous analytical comparison of their performance is lacking. Consequently, there is no concrete understanding of why numerical experiments show that projection-based solvers tend to perform better in many real and synthetic scenarios. In this work, we develop a framework for such analysis, and we use that framework to investigate the comparison of optimization-based and projection-based solvers."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/157014"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","Copyright retained by author(s)"],"dc:rights.uri":["https://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Effects of Data Heterogeneity on Distributed Linear System Solvers"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:21:53Z"}