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51.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
52.
53.
54.
Hirohisa Yokota Kenji Kamoto Jun-ichi Igarashi Norihiko Mouri Yutaka Sasaki 《Optical Review》2002,9(1):9-12
A new configuration for an ASE reduction filter in EDFA repeaters for WDM optical transmission systems using optical fiber grating couplers (FGCs) was proposed and first demonstrated. The filtering characteristics of the proposed filter for amplified single wavelength signal and 2-channel WDM signals using EDFA were identified. It was found that the filter was effective to improve SNR in optical domain by reducing ASE noise. The required FGC characteristics for the filter were theoretically predicted under the condition that the total filter loss did not exceed 3 dB. More than 70% of drop efficiency was required in each FGC for the application of the proposed filter to an 8-channel WDM system using EDFA repeaters. 相似文献
55.
High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting
the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of
the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation
problems are taken into account to emphasize the main features of the proposed methods.
AMS subject classification (2000) 65L10, 65L12, 65L50 相似文献
56.
本文提出等效远场的可变孔径方法,由测量光纤远场累积分布求得模场半径。并且利用Petermann关于模场半径的新定义,推出了一种对非高斯模场分布也适用的求模场半径的方法。实验表明,这种测量方法简便可靠,在不同的制备端面下,重复测量的标准误差小于0.04μm。 相似文献
57.
Boniface Nkemzi 《Mathematical Methods in the Applied Sciences》2006,29(9):1053-1080
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
58.
随着光纤传输技术的不断发展,在传输领域中光传输已占主导地位。光纤存在巨大的频带资源和优异的传输性能,是实现高速、大容量传输的最理想的传输媒质。对光纤传输的要求是传的距离越远越好。从光纤传输距离的计算方法入手,结合影响传输距离的几个因素来分析可以从哪些方面入手来延长光纤通信的传输距离。 相似文献
59.
A simple method of determining ultra-trace Au in natural water was presented by using graphite furnace atomic absorption spectrophotometry (GFAAS) after in situ enrichment with thiol cotton fiber (TCF). The sample solution was adjusted to pH 1.5-2.0 with HCl, then the water sample was passed through a column packed with 0.10-0.20 g TCF and the flow rate was controlled at 20-40 ml min−1. The effects of interferences, such as complexing and oxidizing agents and other elements adsorbed on TCF were overcome by chemical treatments prior to the desorption of Au. The adsorbed Au was adsorbed with 2.0 ml hot acid, then it was extracted with 1.00 ml methyl isobutylketone (MIBK). For a 5 l water sample, the detection limit of Au is 0.02 ng l−1. The relative standard deviation (R.S.D.) for the determination of 1.44 ng l−1 Au was 9.4%.The method was applied to determine ultra-trace Au both in suspended phase and soluble phase in natural water, the concentrations of total Au in natural water samples range from 0.51 to 67.82 ng l−1. The recovery of added 0.50-6.00 ng l−1 Au was 80-95%. The method is useful in prospecting for Au deposits by means of hydrogeochemical methods. The enrichment is carried out in the field, and then the determination of Au is completed later in the laboratory. 相似文献
60.
A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given. 相似文献