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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, a general method to calculate analytically the cross section of any shape of a microcell is presented, which is the generalization of existing zone-integration methods based on the linear approximation.
Abstract: A general method to calculate analytically the cross section of any shape of a microcell is presented. This method is the generalization of existing zone-integration methods based on the linear approximation. This method is useful for calculating joint densities of states in metals as well as dynamical susceptibilities and dielectric functions when the Fermi surface splits microcells into contributing and noncontributing volumes. It may also prove useful for calculating densities of states in crystals of lower symmetries.

17 citations

Journal ArticleDOI
TL;DR: In this paper, a beam propagation method based on the Beam Propagation Method (BPM) was proposed to take the nonlinearity of optical diffraction tomography into account.
Abstract: In Optical diffraction tomography, the multiply scattered field is a nonlinear function of the refractive index of the object. The Rytov method is a linear approximation of the forward model, and is commonly used to reconstruct images. Recently, we introduced a reconstruction method based on the Beam Propagation Method (BPM) that takes the nonlinearity into account. We refer to this method as Learning Tomography (LT). In this paper, we carry out simulations in order to assess the performance of LT over the linear iterative method. Each algorithm has been rigorously assessed for spherical objects, with synthetic data generated using the Mie theory. By varying the RI contrast and the size of the objects, we show that the LT reconstruction is more accurate and robust than the reconstruction based on the linear model. In addition, we show that LT is able to correct distortion that is evident in Rytov approximation due to limitations in phase unwrapping. More importantly, the capacity of LT in handling multiple scattering problem are demonstrated by simulations of multiple cylinders using the Mie theory and confirmed by experimental results of two spheres.

17 citations

Patent
18 Jan 2002
TL;DR: In this paper, a method and system for estimating a logarithm of a number where a linear approximation of a fractional part is determined and the linear approximation is implemented in a single polynomial function is presented.
Abstract: The present invention is directed to methods and systems for estimating the log base-2 of a fixed point binary number using a single polynomial for an entire possible range of input numbers. An estimation of the log base-2 of a fixed-point binary number in either hardware or software may be implemented using a minimal number of parameters. In particular, a single 2 nd order or greater polynomial may be sufficient to cover an entire range of input values for any arbitrary input word precision. The present invention provides a method and system for estimating a logarithm of a number where a linear approximation of a fractional part is determined and the linear approximation is implemented in a single polynomial function for estimating the fractional part for a range of input values. A circuit for generating an integer part and an estimate of a fractional part of a logarithm may include a shift register for loading a valid input data and for generating an estimate of a fractional part and a counter for loading a total number of bits in an input data and for generating an integer part, wherein the circuit implements a single polynomial for generating an improved estimate of the fractional part.

17 citations

Journal ArticleDOI
TL;DR: Methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes are developed and analyzed.
Abstract: We develop and analyze methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes. The methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes. The novel aspect of the scheme is the construction of a linear approximation to the solution, which is used in projecting the solution from one mesh to another. Extensions to advection-diffusion equations are discussed, where the advection is handled by upwinding. Numerical results validating the theory are also presented.

17 citations

Journal ArticleDOI
TL;DR: It is demonstrated, that the force provides a stabilizing effect if it acts in the opposite direction to the velocity vector, and that the better stability properties take place for the implicit model.

17 citations


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