## Abstract

We consider linear systems of equations, Ax Db, 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 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 converges to a solution when A is singular and may also be used with substantial benefit when A is nearly singular.

Original language | English (US) |
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Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Mathematics of Operations Research |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2014 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Computer Science Applications
- Management Science and Operations Research

## Keywords

- Approximate dynamic programming
- Projected equation
- Regularization
- Simulation
- Singular system
- Sstabilization
- Stochastic algorithm