Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems

• Main Authors: Wang, Mengdi (Contributor), Bertsekas, Dimitri P. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Laboratory for Information and Decision Systems (Contributor)
• Format: Article
• Language: English
• Published: Institute for Operations Research and the Management Sciences (INFORMS), 2015-11-09T14:53:08Z.
• Subjects: Article
• Online Access: Get fulltext

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.
United States. Air Force (Grant GA9550-10-1-0412)
Los Alamos National Laboratory. Information Science and Technology Institute (Grant 67870-001-08)