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J. H. Bramble

Bio: J. H. Bramble is an academic researcher. The author has contributed to research in topics: Matrix splitting & Matrix (mathematics). The author has an hindex of 1, co-authored 1 publications receiving 5446 citations.

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Book
01 Jan 1988
TL;DR: This book provides a clear and simple account of the key ideas and algorithms of reinforcement learning, which ranges from the history of the field's intellectual foundations to the most recent developments and applications.
Abstract: Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

37,989 citations

Book
01 Apr 2003
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Abstract: Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

13,484 citations

Journal ArticleDOI
TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Abstract: A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an ap- plication to a three-dimensional convection problem is presented.

4,991 citations

Journal ArticleDOI
TL;DR: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior – and proves their convergence and optimality for special cases and relation to supervised-learning methods.
Abstract: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage.

4,803 citations

Journal ArticleDOI
TL;DR: A Nyquist criterion is proved that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability, and a method for decentralized information exchange between vehicles is proposed.
Abstract: We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

4,377 citations