Projected Equation Methods for Approximate Solution of Large Linear Systems
Dimitri Bertsekas and Huizhen Yu
Journal of Computational and Applied Mathematics Volume 227, Number 1, pp. 27-50, 2009.

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.

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