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Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.


Papers
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Proceedings ArticleDOI
14 Mar 2007
TL;DR: This work constructs and compares two classes of effective predictive models: piecewise polynomial regression and artifical neural networks, and applies statistical techniques such as clustering, association, and correlation analysis, to understand the application parameter space better.
Abstract: Increasing system and algorithmic complexity combined with a growing number of tunable application parameters pose significant challenges for analytical performance modeling. We propose a series of robust techniques to address these challenges. In particular, we apply statistical techniques such as clustering, association, and correlation analysis, to understand the application parameter space better. We construct and compare two classes of effective predictive models: piecewise polynomial regression and artifical neural networks. We compare these techniques with theoretical analyses and experimental results. Overall, both regression and neural networks are accurate with median error rates ranging from 2.2 to 10.5 percent. The comparable accuracy of these models suggest differentiating features will arise from ease of use, transparency, and computational efficiency.

226 citations

Journal ArticleDOI
TL;DR: Convergence of local and global discretization errors to the Radau polynomial of degree p +1 holds for smooth solutions as p →∞ and is used to construct asymptotically correct a posteriori estimates of spatial discretized errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth.

226 citations

Journal ArticleDOI
TL;DR: The theory of subanalytic sets is used in this article to prove that analytic control systems are controllable, and that for every point p in the state space there exists a piecewise analytic feedback control that steers every state into p.

225 citations

Journal ArticleDOI
TL;DR: In this paper, a data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline, which is optimized with respect to a cross-validation criterion.
Abstract: Summary This paper considers the problem of selecting optimal bandwidths for variable (sample-point adaptive) kernel density estimation. A data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross-validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions.

225 citations

Journal ArticleDOI
TL;DR: It is shown that the stability of the system can be established if a piecewise Lyapunovfunction can be constructed and the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software.
Abstract: Presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software.

224 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
2023917
20222,014
20211,089
20201,147
20191,106