Projected equation methods for approximate solution of large linear systems

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44 Scopus citations

Abstract

We consider linear systems of equations and solution approximations derived by projection on a low-dimensional subspace. We propose stochastic iterative algorithms, based on simulation, which converge to the approximate solution and are suitable for very large-dimensional problems. The algorithms are extensions of recent approximate dynamic programming methods, known as temporal difference methods, which solve a projected form of Bellman's equation by using simulation-based approximations to this equation, or by using a projected value iteration method.

Original languageEnglish (US)
Pages (from-to)27-50
Number of pages24
JournalJournal of Computational and Applied Mathematics
Volume227
Issue number1
DOIs
StatePublished - May 1 2009

Keywords

  • Dynamic programming
  • Jacobi method
  • Linear equations
  • Projected equations
  • Simulation
  • Temporal differences
  • Value iteration

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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