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Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.


Papers
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Book ChapterDOI
20 Aug 2002
TL;DR: This work proposes a solution for the PQO problem for the case when the cost functions are linear in the given parameters, and a solution based on modification of an existing query optimizer, which is minimally intrusive.
Abstract: The cost of a query plan depends on many parameters, such as predicate selectivities and available memory, whose values may not be known at optimization time. Parametric query optimization (PQO) optimizes a query into a number of candidate plans, each optimal for some region of the parameter space. We first propose a solution for the PQO problem for the case when the cost functions are linear in the given parameters. This solution is minimally intrusive in the sense that an existing query optimizer can be used with minor modifications: the solution invokes the conventional query optimizer multiple times, with different parameter values. We then propose a solution for the PQO problem for the case when the cost functions are piecewise-linear in the given parameters. The solution is based on modification of an existing query optimizer. This solution is quite general, since arbitrary cost functions can be approximated to piecewise linear form. Both the solutions work for an arbitrary number of parameters.

76 citations

Journal ArticleDOI
TL;DR: In this article, the authors study the global behavior of the piecewise linear area-preserving transformation x 1 = 1 − y 0 + | x 0 |, y 1 = x 0, and show that there are infinitely many invariant polygons surrounding an elliptic fixed point.

76 citations

Journal ArticleDOI
Hanif D. Sherali1
TL;DR: This paper proposes a new pedagogically simpler modification of the standard text-book modeling strategy that constructs its convex hull representation, thereby rendering it locally ideal and exhibits a nonsingular linear transformation that equivalently converts the proposed model into Padberg's formulation.

76 citations

Journal ArticleDOI
TL;DR: A finite element solution based on the Galerkin method was developed for the Saint-Venant equations that approximately govern unsteady flow in rigid open channels as discussed by the authors, and applications to test problems confirmed stability provided that time steps were not so large as to render invalid the Newton linearization scheme used for the friction factor.
Abstract: A finite element solution based on the Galerkin method was developed for the Saint-Venant equations that approximately govern unsteady flow in rigid open channels. A predictor-corrector solution scheme produced theoretically stable and convergent results, and applications to test problems confirmed stability provided that time steps were not so large as to render invalid the Newton linearization scheme used for the friction factor. Linear elements were adequate for all problems solved. Time step limitations to produce accurate results were closely related to: (1) The degree to which piecewise linear functions describing the variation of depth and discharge in time could be fit to the actual curvilinear functions; and (2) the value given to the time step weighting factor. Values of this factor near 0.5 gave the best results.

76 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical analysis on DL-based channel estimation for single-input multiple-output (SIMO) systems is presented to understand and interpret its internal mechanisms, and the authors demonstrate that DL based channel estimation does not restrict to any specific signal model and asymptotically approaches to the minimum mean-squared error (MMSE) estimation without requiring any prior knowledge of channel statistics.
Abstract: Deep learning (DL) has emerged as an effective tool for channel estimation in wireless communication systems, especially under some imperfect environments. However, even with such unprecedented success, DL methods are often regarded as black boxes and are lack of explanations on their internal mechanisms, which severely limits their further improvement and extension. In this paper, we present preliminary theoretical analysis on DL based channel estimation for single-input multiple-output (SIMO) systems to understand and interpret its internal mechanisms. As deep neural network (DNN) with rectified linear unit (ReLU) activation function is mathematically equivalent to a piecewise linear function, the corresponding DL estimator can achieve universal approximation to a large family of functions by making efficient use of piecewise linearity. We demonstrate that DL based channel estimation does not restrict to any specific signal model and asymptotically approaches to the minimum mean-squared error (MMSE) estimation in various scenarios without requiring any prior knowledge of channel statistics. Therefore, DL based channel estimation outperforms or is at least comparable with traditional channel estimation, depending on the types of channels. Simulation results confirm the accuracy of the proposed interpretation and demonstrate the effectiveness of DL based channel estimation under both linear and nonlinear signal models.

76 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023179
2022377
2021312
2020353
2019329
2018297