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.

Two-dimensional cubic convolution

Abstract: The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2]/spl times/[-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.

On the nonlocality of the fractional Schrödinger equation

Abstract: A number of papers over the past eight years have claimed to solve the fractional Schrodinger equation for systems ranging from the one-dimensional infinite square well to the Coulomb potential to one-dimensional scattering with a rectangular barrier. However, some of the claimed solutions ignore the fact that the fractional diffusion operator is inherently nonlocal, preventing the fractional Schrodinger equation from being solved in the usual piecewise fashion. We focus on the one-dimensional infinite square well and show that the purported ground state, which is based on a piecewise approach, is definitely not a solution of the fractional Schrodinger equation for the general fractional parameter α. On a more positive note, we present a solution to the fractional Schrodinger equation for the one-dimensional harmonic oscillator with α=1.

Matching by Tone Mapping: Photometric Invariant Template Matching

Abstract: A fast pattern matching scheme termed matching by tone mapping (MTM) is introduced which allows matching under nonlinear tone mappings. We show that, when tone mapping is approximated by a piecewise constant/linear function, a fast computational scheme is possible requiring computational time similar to the fast implementation of normalized cross correlation (NCC). In fact, the MTM measure can be viewed as a generalization of the NCC for nonlinear mappings and actually reduces to NCC when mappings are restricted to be linear. We empirically show that the MTM is highly discriminative and robust to noise with comparable performance capability to that of the well performing mutual information, but on par with NCC in terms of computation time.

Piecewise approximate circuit simulation

Abstract: Conventional circuit simulation methods are inflexible and slow, especially for large circuits. Piecewise approximate circuit simulation, an alternative that can be more efficient and allows variable accuracy in the simulation process, is discussed. Thus, the tradeoff between accuracy and CPU time is in the hands of the user. SPECS (simulation program for electronic circuits and systems) is the prototype implementation of a piecewise approximate, tree/link based, event driven, variable accuracy circuit simulation algorithm that uses table models for device evaluation. The models can be built at various levels of accuracy, and concomitant levels of precision are reflected in the simulation results. SPECS has been benchmarked on some large, industrial circuits and has proven to be an efficient and reliable simulator. However, it suffers a penalty in run time while simulating stiff circuits, or circuits with a wide range of time constants. The authors present enhanced algorithms used in SPECS to ensure efficient steady-state computation for stiff circuits. >

Superconvergence of mixed finite element methods for optimal control problems

Abstract: T. In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity assumptions are presented and applied to error estimation by using an operator interpolation technique. We derive L 2 superconvergence properties for the flux functions along the Gauss lines and for the scalar functions at the Gauss points via mixed projections. Moreover, global L 2 superconvergence results are obtained by virtue of an interpolation postprocessing technique. Thus, based on these superconvergence estimates, some asymptotic exactness a posteriori error estimators are presented for the mixed finite element methods. Finally, some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence.