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Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.


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Journal ArticleDOI
TL;DR: In this paper, a discrete form of the flux-divergence operator is developed to compute advection of tracers on spherical hexagonal-pentagonal grids, where the distribution of a tracer over the upwind side of a cell face is linearly approximated using a nodal value and a gradient at a computational node on the up-wind side.
Abstract: A discrete form of the flux-divergence operator is developed to compute advection of tracers on spherical hexagonal–pentagonal grids. An upwind-biased advection scheme based on a piecewise linear approximation for one-dimensional regular grids is extended simply for spherical hexagonal–pentagonal grids. The distribution of a tracer over the upwind side of a cell face is linearly approximated using a nodal value and a gradient at a computational node on the upwind side. A piecewise linear approximation is relaxed to a local linear approximation, and the relaxation precludes the complicated conditional branching present in remapping schemes. Results from a cosine bell advection test show that the new scheme compares favorably with other upwind-biased schemes for spherical hexagonal–pentagonal grids.

79 citations

Proceedings ArticleDOI
27 Jun 2011
TL;DR: A closed-form approximation to the full SLAM problem is proposed, under the assumption that the relative position and the relative orientation measurements are independent, and it is demonstrated that such refinement is often unnecessary, since the linear estimate is already accurate.
Abstract: This article investigates the problem of Simultaneous Localization and Mapping (SLAM) from the perspective of linear estimation theory. The problem is first formulated in terms of graph embedding: a graph describing robot poses at subsequent instants of time needs be embedded in a three-dimensional space, assuring that the estimated configuration maximizes measurement likelihood. Combining tools belonging to linear estimation and graph theory, a closed-form approximation to the full SLAM problem is proposed, under the assumption that the relative position and the relative orientation measurements are independent. The approach needs no initial guess for optimization and is formally proven to admit solution under the SLAM setup. The resulting estimate can be used as an approximation of the actual nonlinear solution or can be further refined by using it as an initial guess for nonlinear optimization techniques. Finally, the experimental analysis demonstrates that such refinement is often unnecessary, since the linear estimate is already accurate.

79 citations

Posted Content
TL;DR: An algorithm is developed which permits stable deep Q-learning for continuous control without any of the tricks conventionally used (such as target networks, adaptive gradient optimizers, or using multiple Q functions).
Abstract: Deep Q-Learning (DQL), a family of temporal difference algorithms for control, employs three techniques collectively known as the `deadly triad' in reinforcement learning: bootstrapping, off-policy learning, and function approximation. Prior work has demonstrated that together these can lead to divergence in Q-learning algorithms, but the conditions under which divergence occurs are not well-understood. In this note, we give a simple analysis based on a linear approximation to the Q-value updates, which we believe provides insight into divergence under the deadly triad. The central point in our analysis is to consider when the leading order approximation to the deep-Q update is or is not a contraction in the sup norm. Based on this analysis, we develop an algorithm which permits stable deep Q-learning for continuous control without any of the tricks conventionally used (such as target networks, adaptive gradient optimizers, or using multiple Q functions). We demonstrate that our algorithm performs above or near state-of-the-art on standard MuJoCo benchmarks from the OpenAI Gym.

79 citations

Journal ArticleDOI
TL;DR: A frequency domain identification procedure is proposed where the model parameters are computed by DFT of appropriately transformed data and bounds on the the partial sum operators and on the L ∞ norm of the approximation error are derived.

78 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202229
202197
2020134
2019124
2018147