Topic
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.
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TL;DR: This paper presents an overview of the research progress in global optimization during the last 5 years, and a brief account of the recent research contributions, and the recently proposed novel generalized BB framework.
210 citations
TL;DR: In this article, the authors propose a method for the analysis of spatial data with sharp changes in the underlying covariance structure by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary.
Abstract: In many problems in geostatistics the response variable of interest is strongly related to the underlying geology of the spatial location. In these situations there is often little correlation in the responses found in different rock strata, so the underlying covariance structure shows sharp changes at the boundaries of the rock types. Conventional stationary and nonstationary spatial methods are inappropriate, because they typically assume that the covariance between points is a smooth function of distance. In this article we propose a generic method for the analysis of spatial data with sharp changes in the underlying covariance structure. Our method works by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary, but the data are assumed independent across regions. Uncertainty in the number of disjoint regions, their shapes, and the model within regions is dealt with in a fully Bayesian fashion. We illustrate our approach on a previously ...
210 citations
TL;DR: In this paper, a high-order extension of the second-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems is presented.
Abstract: We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000) pp. 241--282].
The method is derived independently of the specific piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results by focusing on the new third-order central weighted essentially nonoscillatory (CWENO) reconstruction presented in [D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 21 (1999), pp. 294--322]. The numerical results we present show the desired accuracy, high resolution, and robustness of our method.
210 citations
TL;DR: This paper uses higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and uses the Simpson method to design a higher order algorithm for the fractionsal differential equations.
209 citations
TL;DR: In this paper, the authors present a unified framework for performing local analysis of grazing bifurcations in n-dimensional piecewise-smooth systems of ODEs, where a periodic orbit has a point of tangency with a smooth (n−1)-dimensional boundary dividing distinct regions in phase space where the vector field is smooth.
208 citations