Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Accelerating simulation of differential equation systems having continuous behavior

Abstract: An innovative method is taught for accelerating the simulation rate of differential equation systems having behavior piece-wise continuous in both value and time. Specifically, a system of differential equations representing the behavior of a physical system comprised of electronic, optical, or mechanical components may be simulated more rapidly using this method. The method utilizes incremental and iterative reconfiguration of digital logic wherein each configuration of the logic operates to yield a unique future value or range of values for each time-varying state variable within a system of equations representing a linear approximation of the original differential equation system for state variable values defined initially or at the onset of an iteration. Various configurations of the digital logic may be pre-computed or computed on demand, optionally caching such configurations for subsequent reuse.

Model reduction of linear interval systems using Pade approximation

Abstract: This paper presents model reduction of linear interval system using Pade approximation method. In the first part a full Pade approximation method for interval system is presented, where as in the second part stable Pade approximation is discussed. A numerical example illustrates the procedure.

An enhanced linear Kalman filter EnLKF algorithm for parameter estimation of nonlinear rational models

Abstract: In this study, an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation The mechanism of linear Kalman filter LKF with point data processing is adopted to develop a new recursive algorithm The novelty of the enhanced linear Kalman filter EnLKF in short and distinguished from extended Kalman filter EKF is that it is not formulated from the routes of extended Kalman Filters to approximate nonlinear models by linear approximation around operating points through Taylor expansion and also it includes LKF as its subset while linear models have no correlated errors in regressor terms No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research Three simulated examples are selected to bench-test the performance of the algorithm In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications It should be noted that this approach is fundamentally different from those using linearisation to approximate nonlinear models and then conduct state/parameter estimate