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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.


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Proceedings ArticleDOI
18 Jun 1984
TL;DR: An algorithm is presented for the efficient and accurate simulation of switched-mode piecewise-li near systems, a subclass of which includes regulated energy-storage dc-to-dc converters that leads to significant improvements in computational efficiency and accuracy.
Abstract: An algorithm is presented for the efficient and accurate simulation of switched-mode piecewise-li near systems, a subclass of which includes regulated energy-storage dc-to-dc converters. Three key features of the new algorithm that lead to significant improvements in computational efficiency and accuracy are: (1) a state-transition-matrix table-lookup scheme to solve differential equations describing the system, (2) a modified binary-search strategy to obtain an initial estimate of the instant at which the system topology switches, and (3) a quadratic extrapolation for the accurate final determination of the switching instant. The computational efficiency of a program using the new algorithm is demonstrated by comparing its execution time with that of a program employing a standard fixed-step-size integration algorithm. The accuracy of the new algorithm is verified by comparing results obtained from the simulations with results obtained analytically, and by comparing data from the simulation of two different regulated converters with data measured experimentally.

57 citations

Journal ArticleDOI
TL;DR: It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function.

57 citations

Journal ArticleDOI
TL;DR: This work extends the least angle regression further to handle Cox's proportional hazards model, and defines a path modification, which leads to the solution path of the elastic net regularized log partial likelihood.
Abstract: For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

57 citations

Journal ArticleDOI
TL;DR: These methods develop general methodologies for the minimal time routing problem of a vessel moving in stationary or time dependent environments, respectively, which result in piecewise continuous optimal policies.
Abstract: We develop general methodologies for the minimal time routing problem of a vessel moving in stationary or time dependent environments, respectively. Local optimality considerations, combined with global boundary conditions, result in piecewise continuous optimal policies. In the stationary case, the velocity of the traveling vessel within each subregion depends only on the direction of motion. Variational calculus is used to derive the geometry of piecewise linear extremals. For the time dependent problem, the speed of the vessel within each subregion is assumed to be a known function of time and the direction of motion. Optimal control theory is used to reveal the nature of piecewise continuous optimal policies.

57 citations

Journal ArticleDOI
TL;DR: This work introduces a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces that enables arbitrary singularities to be represented at vertices and removes the bound imposed on the complexity of singularities that a vertex can represent by its connectivity.
Abstract: Accurately representing higher-order singularities of vector fields defined on piecewise linear surfaces is a non-trivial problem. In this work, we introduce a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces. The scheme enables arbitrary singularities to be represented at vertices. The representation can be considered as a facet-based "encoding" of vector fields on piecewise linear surfaces. The vector field is described in polar coordinates over each facet, with a facet edge being chosen as the reference to define the angle. An integer called the period jump is associated to each edge of the triangulation to remove the ambiguity when interpolating the direction of the vector field between two facets that share an edge. To interpolate the vector field, we first linearly interpolate the angle of rotation of the vectors along the edges of the facet graph. Then, we use a variant of Nielson's side-vertex scheme to interpolate the vector field over the entire surface. With our representation, we remove the bound imposed on the complexity of singularities that a vertex can represent by its connectivity. This bound is a limitation generally exists in vertex-based linear schemes. Furthermore, using our data structure, the index of a vertex of a vector field can be combinatorily determined

57 citations


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