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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors presented an algorithm for off-line estimation of route-level travel times for uninterrupted traffic flow facilities, such as motorway corridors, based on time series of traffic-speed observations taken from the sections that constitute a route.
Abstract: An algorithm is presented for off-line estimation of route-level travel times for uninterrupted traffic flow facilities, such as motorway corridors, based on time series of traffic-speed observations taken from the sections that constitute a route. The proposed method is an extension of the widely used trajectory method. The novelty of the presented method is that trajectories are based on the assumption of piecewise linear (and continuous at section boundaries) vehicle speeds rather than piecewise constant (and discontinuous at section boundaries) speeds. From these assumptions, mathematical expressions are derived that describe the trajectories within each section. These expressions can be used to replace their existing counterparts in the traditional trajectory methods. A comparison of the accuracy of the new method and of the existing method was carried out by using simulated data. This comparison showed that the root-mean-square error (RMSE) value for the new method is about half the RMSE value for the existing method. When this RMSE is decomposed in a bias and a residual error, it turns out that the existing method significantly overestimates the travel time. However, the largest part of the reduction of the RMSE value is still caused by a reduction of the residual error. In other words, if both methods are corrected for their bias, the new method performs significantly better.
155 citations
TL;DR: A finite element method for the approximation of second order elliptic problems on composite grids based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges of one the grids is proposed.
Abstract: In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
155 citations
TL;DR: In this paper, an explicit representation of a piecewise rational quadratic function is developed which produces a monotonic interpolant to given monotonicity data. But this method is not suitable for the case of complex data.
Abstract: An explicit representation of a piecewise rational quadratic function is developed which produces a monotonic interpolant to given monotonic data. The explicit representation means that the piecewise monotonic interpolant is easily constructed and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, the use of the method is justified by an 0(h) convergence result .
154 citations
TL;DR: A series expansion is derived for the potential distribution, caused by a dipole source in a multilayered sphere with piecewise constant conductivity, by first calculating an asymptotic approximation of the potential and using the so-called addition-subtraction method.
Abstract: A series expansion is derived for the potential distribution, caused by a dipole source in a multilayered sphere with piecewise constant conductivity. When the radial coordinate of the source approaches the radial coordinate of the field point the spherical harmonics expansion converges only very slowly. It is shown how the convergence can be improved by first calculating an asymptotic approximation of the potential and using the so-called addition-subtraction method. Since the asymptotic solution is an approximation of the true solution, it gives some insight on the dependence of the potential on the conductivities. The formulas are given in Cartesian coordinates, so that difficulties with coordinate transformations are avoided. Attention is paid to the (fast) computation of the partial derivatives of the potential, which is useful for inverse algorithms. >
154 citations
TL;DR: In this article, the delay-dependent stability problem of linear continuous/discrete systems with time-varying delay is investigated based on a piecewise analysis method (PAM), in which the variation interval of the time delay is firstly divided into several subintervals.
Abstract: The delay-dependent stability problem of linear continuous/discrete systems with time-varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay-dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results. Copyright © 2008 John Wiley & Sons, Ltd.
153 citations