Projected equation methods for approximate solution of large linear systems

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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. © 2008 Elsevier B.V. All rights reserved.

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Bertsekas, D. P., & Yu, H. (2009). Projected equation methods for approximate solution of large linear systems. Journal of Computational and Applied Mathematics, 227(1), 27–50. https://doi.org/10.1016/j.cam.2008.07.037

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