Linear approximation

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

Iterative Linear AC Power Flow Solution for Fast Approximate Outage Studies

Abstract: A fast approximate method is presented for solving the ac power flow problem for line and generator outages. The method is significantly more accurate than any linear approximation and significantly faster than the Newton-Raphson method for an approximate solution. The method has applications in system planning and operations where approximate ac power flow solutions are acceptable. The method is applicable to system planning for rapid location of design criteria violations and it is particularly well adapted for system operation use as an on-line security monitor. Efficiency is achieved through decoupling of real and reactive power equations, sparse matrix methods, an experimentally determined iteration scheme and the use of the matrix inversion lemma to simulate the effect of branch outages.

Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers

Abstract: In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.

Optimal approximation of linear systems by a differential evolution algorithm

Abstract: The problem of optimally approximating linear systems is solved by a differential evolution algorithm (DEA) incorporating a search-space expansion scheme. The optimal approximate rational model with/without a time delay for a system described by its rational or irrational transfer function is sought such that a frequency-domain L/sup 2/-error criterion is minimized. The distinct feature of the proposed model approximation approach is that the search-space expansion scheme can enhance the possibility of converging to a global optimum in the DE search. This feature and the chosen frequency-domain error criterion make the proposed approach quite efficacious for optimally approximating unstable and/or nonmimimum-phase linear systems. The simplicity and robustness of the modified DEA in terms of easy implementation and minimum assumptions on search space are demonstrated by two numerical examples.

Algorithms for bestL 1 andL ∞ linear approximations on a discrete set

Abstract: This paper supplies algorithms for the best approximation to a real-valued function, defined as a table of values, by a linear approximating function in both theL1 andL∞ norms. The algorithms are modified simplex algorithms which due to the particular structures of the tableaux have been condensed and require minimal storage space. Both algorithms are given asAlgol procedures and sample times are noted for several examples.