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.

A Padé-based algorithm for overcoming the Gibbs phenomenon

Abstract: Truncated Fourier series and trigonometric interpolants converge slowly for functions with jumps in value or derivatives The standard Fourier–Pade approximation, which is known to improve on the convergence of partial summation in the case of periodic, globally analytic functions, is here extended to functions with jumps The resulting methods (given either expansion coefficients or function values) exhibit exponential convergence globally for piecewise analytic functions when the jump location(s) are known Implementation requires just the solution of a linear system, as in standard Pade approximation The new methods compare favorably in experiments with existing techniques

Optimal control of piecewise deterministic markov process

Abstract: The trajectories of piecewise deterministic Markov processes are solutions of an ordinary (vector)differential equation with possible random jumps between the different integral curves. Both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting of continuous, jump and terminal costs. A limiting form of the Hamilton-Jacobi-Bellman partial differential equation is shown to be a necessary and sufficient optimality condition. The existence of an optimal strategy is proved and acharacterization of the value function as supremum of smooth subsolutions is also given. The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter by dualit

Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws

Abstract: We discover that the choice of a piecewise polynomial reconstruction is crucial in computing solutions of nonconvex hyperbolic (systems of) conservation laws. Using semidiscrete central-upwind schemes, we illustrate that the obtained numerical approximations may fail to converge to the unique entropy solution or the convergence may be so slow that achieving a proper resolution would require the use of (almost) impractically fine meshes. For example, in the scalar case, all computed solutions seem to converge to solutions that are entropy solutions for some entropy pairs. However, in most applications, one is interested in capturing the unique (Kruzhkov) solution that satisfies the entropy condition for all convex entropies. We present a number of numerical examples that demonstrate the convergence of the solutions, computed with the dissipative second-order minmod reconstruction, to the unique entropy solution. At the same time, more compressive and/or higher-order reconstructions may fail to resolve composite waves, typically present in solutions of nonconvex conservation laws, and thus may fail to recover the Kruzhkov solution. In this paper, we propose a simple and computationally inexpensive adaptive strategy that allows us to simultaneously capture the unique entropy solution and to achieve a high resolution of the computed solution. We use the dissipative minmod reconstruction near the points where convexity changes and utilize a fifth-order weighted essentially nonoscillatory (WENO5) reconstruction in the rest of the computational domain. Our numerical examples (for one- and two-dimensional scalar and systems of conservation laws) demonstrate the robustness, reliability, and nonoscillatory nature of the proposed adaptive method.

Poincar´ e-friedrichs inequalities for piecewise h 1 functions ∗

Abstract: Poincare-Friedrichs inequalities for piecewise H 1 functions are established. They can be applied to classical nonconforming finite element methods, mortar methods, and discontinuous Galerkin methods.

A plane-sweep strategy for the 3d reconstruction of buildings from multiple images

Abstract: A new method is described for automatically reconstructing a 3D piecewise planar model from multiple images of a scene. The novelty of the approach lies in the use of inter-image homographies to validate and best estimate planar facets, and in the minimal initialization requirements — only a single 3D line with a textured neighbourhood is required to generate a plane hypothesis. The planar facets enable line grouping and also the construction of parts of the wireframe which were missed due to the inevitable shortcomings of feature detection and matching. The method allows a piecewise planar model of a scene to be built completely automatically, with no user intervention at any stage, given only the images and camera projection matrices as input. The robustness and reliability of the method are illustrated on several examples, from both aerial and interior views.