Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems
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Author(s)
Wang, Mengdi
Bertsekas, Dimitri P.
Date Issued
May 2013
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Wang, Mengdi, and Dimitri P. Bertsekas. “Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems.” Mathematics of OR 39, no. 1 (February 2014): 1–30.
Version
Author's final manuscript
Abstract
We consider linear systems of equations, Ax = b, with an emphasis on the case where A is singular. Under certain conditions, necessary as well as sufficient, linear deterministic iterative methods generate sequences {x[subscript k]} that converge to a solution as long as there exists at least one solution. This convergence property can be impaired when these methods are implemented with stochastic simulation, as is often done in important classes of large-scale problems. We introduce additional conditions and novel algorithmic stabilization schemes under which {x[subscript k]} converges to a solution when A is singular and may also be used with substantial benefit when A is nearly singular.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/moor.2013.0596
