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Linear approximation

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


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Book ChapterDOI
07 Jun 2004
TL;DR: In this article, the authors show how to approximate a separable concave minimization problem over a general closed ground set by a single piecewise linear minimization, where the approximation is to arbitrary 1+e precision in optimal cost.
Abstract: We show how to approximate a separable concave minimization problem over a general closed ground set by a single piecewise linear minimization problem. The approximation is to arbitrary 1+e precision in optimal cost. For polyhedral ground sets in \(\mathbb{R}^n_+\) and nondecreasing cost functions, the number of pieces is polynomial in the input size and proportional to 1/log(1+e). For general polyhedra, the number of pieces is polynomial in the input size and the size of the zeroes of the concave objective components.

25 citations

Journal ArticleDOI
TL;DR: Discusses the allocation of the available capacity of a statistical multiplexer to serve a number of heterogeneous on-off sources, with the cell loss rate as the performance criterion, and derived computationally efficient bounds and asymptotic approximations for thecell loss rate.
Abstract: Discusses the allocation of the available capacity of a statistical multiplexer to serve a number of heterogeneous on-off sources, with the cell loss rate as the performance criterion. In order to avoid using potentially lengthy simulations, the authors have derived computationally efficient bounds and asymptotic approximations for the cell loss rate. The union of all partitions of the available capacity which satisfies the capacity bound and the performance criterion is defined as the capacity region. Both linear approximation and nonlinear approximation of the capacity region are investigated. It is shown that the linear approximation is reasonably accurate when the activity factors of the sources are not too high (less than 0.8). For the case where the linear approximation appears too optimistic, a simple nonlinear approximation for determining the capacity region is suggested. The accuracy of the method is demonstrated using numerical examples. >

25 citations

Journal ArticleDOI
TL;DR: A systematic optimization methodology for the Control Structure Selection Problem (CSSP) is presented that improves the accuracy of calculations and reduces computational time and effort necessary.

25 citations

Journal ArticleDOI
TL;DR: This work improves the linear approximation scheme, leading to a unified implementation for rotation and vectoring, where fully parallel tree multipliers are used instead of the second half of CORDIC iterations.
Abstract: The unfolded and pipelined CORDIC is a high-performance hardware element that produces a wide variety of one and two argument functions with high throughput. The reduction in delay, power, and area (cost) are of significant interest regarding this module due to its high demand for resources. The linear approximation to rotation has been proposed to achieve such reductions. However, the schemes for rotation (multiplication) and vectoring (division) complicate the implementation in a single unit. In this work, we improve the linear approximation scheme, leading to a unified implementation for rotation and vectoring, where fully parallel tree multipliers are used instead of the second half of CORDIC iterations. We also combine the linear approximation to rotation with the scale factor compensation so that the compensation is concurrently performed with the rotation process. We then extend the method to 3D CORDIC. Such an extension is not straightforward due to the lack of existing analytical expressions for the convergence of the algorithm. A comparison, using a rough area-time model and synthesis results, shows that our proposals may achieve significant reductions in delay, with no increase in area, in actual implementations.

25 citations

Journal ArticleDOI
TL;DR: In this article, the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling were compared.
Abstract: (abridged) We study the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling. We use ray-tracing through the Millennium Simulation to calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare the results from ray-tracing to semi-analytic predictions. We find: (i) The linear approximation provides an excellent fit to cosmic-shear power spectra as long as the actual matter power spectrum is used as input. Common fitting formulae, however, strongly underestimate the cosmic-shear power spectra. Halo models provide a better fit to cosmic shear-power spectra, but there are still noticeable deviations. (ii) Cosmic-shear B-modes induced by Born corrections and lens-lens coupling are at least three orders of magnitude smaller than cosmic-shear E-modes. Semi-analytic extensions to the linear approximation predict the right order of magnitude for the B-mode. Compared to the ray-tracing results, however, the semi-analytic predictions may differ by a factor two on small scales and also show a different scale dependence. (iii) The linear approximation may under- or overestimate the galaxy-galaxy-lensing shear signal by several percent due to the neglect of magnification bias, which may lead to a correlation between the shear and the observed number density of lenses. We conclude: (i) Current semi-analytic models need to be improved in order to match the degree of statistical accuracy expected for future weak-lensing surveys. (ii) Shear B-modes induced by corrections to the linear approximation are not important for future cosmic-shear surveys. (iii) Magnification bias can be important for galaxy-galaxy-lensing surveys.

25 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202229
202197
2020134
2019124
2018147