Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

Projection functions for particle‐grid methods

Abstract: Random walk particle methods (RWPM) can be used in operator splitting schemes to simulate reactive solute transport in porous media. Projection functions are used to transfer particle location and mass information to concentrations at selected spatial points. Because of the stochastic nature of RWPM, concentration estimates made from particle distributions include a “noisy” error component. In some cases of reactive or density-dependent flows, this type of error may be propagated forward in time. It can be reduced by using larger numbers of particles or by using different projection functions. The effects of using different projection functions or numbers of particles in different flow regimes or dimensions are explored using concentration solutions for a set of one-, two-, and three-dimensional nonreactive test problems. Resulting solutions are compared with analytic results and classical random walk error estimates. A piecewise linear projection function provides a reasonable improvement in accuracy over the more convenient box methods at a modest increase in cost. The support of the projection functions should be O(Δx) to avoid excessive smearing. Multidimensional projection functions may be advantageously formed by products of different one-dimensional projection functions.

Development and optimization of piecewise linear discriminants for the automated detection of chemical species

Abstract: A pattern recognition technique based on piecewise linear discriminant analysis (PLDA) is described. Algorithms for the calculation and optimization of piecewise linear discriminants are presented. A simplex optimization of the individual discriminants is described, and a new method to optimize a piecewise linear discriminant is proposed and shown to produce significantly improved results over the nonoptimized method. This methodology is demonstrated through the use of a set of Fourier transform infrared interferograms collected by a remote sensor

Optimal control with limited controls

Abstract: We consider a linear discrete-time optimal control problem where the control is limited in terms of the number of times it can be applied. We assume an additive quadratic performance criterion that does not penalize the control directly, and show that for a scalar plant driven by an independent additive Gaussian noise the optimal control is piecewise linear based on some offline computed thresholds on the optimal estimate of the plant state which can be generated by a Kalman filter.

The Hicksian floor–roof model for two regions linked by interregional trade

Abstract: The Hicksian multiplier–accelerator model with the original floor–roof limits to investments is studied for the case of two regions linked by interregional trade. The result is a piecewise linear continuous four dimensional map, which is reduced to three dimensions through the choice of an appropriate distributed consumption lag. The attractors, basins, and bifurcations of the map are studied under the assumption of a certain symmetry between the regions. The Neimark–Hopf bifurcation for piecewise linear maps is described in detail which gives rise to the appearance of an attracting closed invariant curve homeomorphic to a circle. The structure of resonance regions in the parameter space are investigated.

Piecewise Linear Models for Switch-Level Simulation

Abstract: Rsim is an efficient logic plus timing simulator that employs the switched resistor transistor model and RC tree analysis to simulate efficiently MOS digital circuits at the transistor level. We investigate the incorporation of piecewise linear transistor models and generalized moments matching into this simulation framework. General piecewise linear models allow more accurate MOS models to be used to simulate circuits that are hard for Rsim. Additionally, they enable the simulator to handle circuits containing bipolar transistors such as ECL and BiCMOS. Nonetheless, the switched resistor model has proved to be efficient and accurate for a large class of MOS digital circuits. Therefore, it is retained as just one particular model available for use in this framework. The use of piecewise linear models requires the generalization of RC tree analysis. Unlike switched resistors, more general models may incorporate gain and floating capacitance. Additionally, we extend the analysis to handle non-tree topologies and feedback. Despite the increased generality, for many common MOS and ECL circuits the complexity remains linear. Thus, this timing analysis can be used to simulate, efficiently, those portions of the circuit that are well described by traditional switch level models, while simultaneously simulating, more accurately, those portions that are not. We present preliminary results from a prototype simulator, Mom. We demonstrate its use on a number of MOS, ECL, and BiCMOS circuits.