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Topic: Asymptotic analysis

In the News (Sat 25 May 13)

 Asymptotic analysis - Wikipedia, the free encyclopedia The asymptotic point of view is basic in computer science, where the question is typically how to describe the resource implication of scaling-up the size of a computational problem, beyond the 'toy' level. An asymptotic expansion of a function f(x) is in practice an expression of that function in terms of an infinite series, the partial sums of which do not (necessarily have to) converge; but such that taking any initial partial sum provides an asymptotic formula for f. Asymptotic expansions typically arise in the approximation of certain integrals (saddle-point method, method of steepest descent) or in the approximation of probability distributions (Edgeworth series). www.wikipedia.org /wiki/Asymptotic   (365 words)

 CMSC 202 Lecture Notes: Asymptotic Analysis This type of analysis is known as asymptotic analysis. Asymptotic analysis is based on the idea that as the problem size grows, the complexity can be described as a simple proportionality to some known function. The reason is that asymptotic analysis ignores constants of proportionality. userpages.umbc.edu /~anastasi/Courses/341/Spr00/Lectures/Asymptotic/asymptotic.html   (1301 words)

 [No title]   (Site not responding. Last check: 2007-11-06) The asymptotic structure of unstrained, laminar, fuel-rich, premixed methane flame is analyzed using a reduced chemical-kinetic mechanism made up of three global steps. In contrast to previous asymptotic analyses of lean flames and moderately rich flames, where the reaction zone of these flamess was presumed to be made up of two layers, for rich flames analyzed here all chemical reaction are presumed to take place in one layer. For values of equivalence ratio greater than 1.3, burning velocities obtained from the asymptotic analysis are found to agree reasonably well with those obtained using a chemical-kinetic mechanism made up of elementary reactions. www.stanford.edu /~hpitsch/abstracts/VeryRichMethaneCombFlame.html   (166 words)

 PSFC/JA-03-5 Abstract   (Site not responding. Last check: 2007-11-06) Asymptotic analysis of dispersion characteristics in two-dimensional metallic photonic band gap structures We present a self-consistent technique for the asymptotic analysis of dispersion curves in two-dimensional (2D) metallic photonic band gap (PBG) structures representing square and triangular arrays of metal rods. The technique is applicable for the structures with rod radii (a), which are small compared to the distance between the rods (b) and to the wavelength (λ). www.psfc.mit.edu /library/03ja/03JA005/03JA005_abs.html   (116 words)

 Asymptotic Analysis Flames   (Site not responding. Last check: 2007-11-06) The rate-ratio asymptotic analysis has been applied to predict the flame structure and extinction diameter for methanol burning in air. The flame structure is shown in the following figure, in which Z is the mixture fraction, with Z = 0 in the atmasphere and Z = 1 in the fuel. The predicted extinction diameters of pure methanol droplets, burning in oxygen-nitrogen mixtures at 300 K, as function of the ambient oxygen mole fraction, for three different pressures, is shown in the following figure; solid curves are for two-step chemistry and points for three-step chemistry. maeweb.ucsd.edu /combustion/NASA/Asymptotic.html   (139 words)

 SPE59312   (Site not responding. Last check: 2007-11-06) Low-frequency asymptotic analysis of seismic reflection from a fluid-saturated medium This paper presents a low-frequency asymptotic formula for the reflection of seismic plane p-wave from a fluid-saturated porous medium. The obtained asymptotic scaling of the frequency-dependent component of the reflection coefficient shows that it is asymptotically proportional to the square root of the product of the reservoir fluid mobility and the frequency of the signal. petroleum.berkeley.edu /papers/patzek/TIPM19R1.htm   (140 words)

 Asymptotic analysis of aircraft wing model in subsonic air flow -- Shubov 66 (4): 319 -- IMA Journal of Applied ... Asymptotic analysis of aircraft wing model in subsonic air flow -- Shubov 66 (4): 319 -- IMA Journal of Applied Mathematics Asymptotic analysis of aircraft wing model in subsonic air flow to the asymptotic and spectral analysis of an aircraft wing imamat.oupjournals.org /cgi/content/abstract/66/4/319   (329 words)

 Doctoral research project Asymptotic analysis of orthogonal polynomials and dynamical ...   (Site not responding. Last check: 2007-11-06) Doctoral research project Asymptotic analysis of orthogonal polynomials and dynamical... Asymptotic analysis of orthogonal polynomials and dynamical systems using Riemann-Hilbert problems. We study a matrix valued extension which has application in the asymptotic analysis of orthogonal polynomials and dynamical systems. www.kuleuven.ac.be /research/researchdatabase/project/3E00/3E000215.htm   (66 words)

 Asymptotic analysis of a particle system with mean-field interaction   (Site not responding. Last check: 2007-11-06) Asymptotic analysis of a particle system with a mean-field interaction For the situation B we prove that all stochastic interacting particles form a single group which moves with an asymptotically constant speed. It appears that due to the present interaction between the particles this speed differs from the mean drift of the free particle motion. www.math.msu.su /%7Emanita/ms_asymp.html   (194 words)

 Asymptotic Analysis of the MMSE Multiuser Detector for Nonorthogonal Multipulse Modulation We analyze the asymptotic performance of the detector and show that, unlike the case of linear modulation, the MMSE detector does not generally approach the generalized maximum-likelihood (GML) detection rule as the noise power vanishes. The probability of error for this detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse decorrelating detector and the MMSE detector. It is shown that for noncoherent binary signaling,in which the multipulse modulation is two-dimensional, the multipulse decorrelating detector is superior to the GML detector asymptotically. www.comsoc.org /comm/private/2001/jan/24_49comm01-mccloud.html   (437 words)

 Lecture 12: Asymptotic complexity A good rule of thumb is: the slower the asymptotic growth rate, the better the algorithm (although this is often not the whole story). This kind of analysis is generally harder, since it involves probabilistic arguments and often requires assumptions about the distribution of inputs that may be difficult to justify. This is a valid criticism of asymptotic analysis and big-O notation. www.cs.cornell.edu /courses/cs312/2003sp/lectures/lec12.html   (2367 words)

 Asymptotic Analysis of Buffered Calcium Diffusion near a Point Source Asymptotic Analysis of Buffered Calcium Diffusion near a Point Source: SIAM Journal on Applied Mathematics Vol. Using perturbation methods, we derive approximations for the ${\rm Ca}^{\rm 2+}$ and buffer profiles in three asymptotic limits: (1) an "excess buffer approximation" (EBA), where the mobility of buffer exceeds that of ${\rm Ca}^{\rm 2+}$ (${\varepsilon}_b \gg {\varepsilon}_c$) and the fast diffusion of buffer toward the ${\rm Ca}^{\rm 2+}$ channel prevents buffer saturation (cf. However, the asymptotic formalism allows derivation for the first time of higher order terms, which are shown numerically to significantly extend the range of validity of these approximations. epubs.siam.org /sam-bin/dbq/article/36899   (437 words)

 [No title]   (Site not responding. Last check: 2007-11-06) In this paper, we provide an asymptotic performance analysis of channel-aware packet scheduling based on extreme value theory. Compared to the exact throughput expression, the asymptotic one, which is applicable to a broader range of fading channels, is more concise and easier to get insights. We also investigate the asymptotic average throughput of the normalized-SNR-based scheduling and prove that the average throughput in this case is less than that in the homogeneous case with a power constraint. users.ece.gatech.edu /~songgc/pub/ata.html   (123 words)

 Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs)   (Site not responding. Last check: 2007-11-06) Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs) The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. An undergraduate knowledge of partial differential equations and functional analysis is assumed. www.textkit.com /0_0198514956.html   (108 words)

 Session FC - Shear Layer Instabilities/Turbulence. Using a nonlinear critical layer analysis, we consider the nonlinear evolution of two-dimensional disturbances to a subsonic compressible mixing layer subjected to a transverse magnetic field, and derive a set of nonlinear equations similar to those found by Goldstein and Leib (JFM 191, pp 481-515, 1988) for an incompressible mixing layer. The unbounded shear flow is found to capture the essential dynamics of the rapid transient growth processes, while excitation by nonmodal mechanisms of nearly neutral modes is found to be important in sustaining high perturbation amplitude at long times. Asymptotic analytical and asymptotic numerical methods have both been described and used to model this shear layer problem. flux.aps.org /meetings/YR99/DFD99/abs/S580.html   (1456 words)

 Citations: Asymptotic analysis of stochastic programs - Shapiro (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath   (Site not responding. Last check: 2007-11-06) Alexander Shapiro, "Asymptotic analysis of stochastic programs," Annals of Operations Research 30 (1991), 169--186. In this area, which one could label asymptotic analysis of stochastic programs, there remain many open questions some of which are technically quite challenging. However much asymptotic analysis might lead to a better understanding of the behavior of the solutions of stochastic programs.... smealsearch.psu.edu /context/9538/0   (131 words)

 [No title]   (Site not responding. Last check: 2007-11-06) This talk presents an asymptotic approach based on the method of compound asymptotic expansions. The asymptotic approximations of solutions of these singularly perturbed problems involve boundary layers in the vicinty of junction regions. Analysis of spectral problems for multi-structures gives accurate asymptotic formulae for the first eigenfrequencies. www.math.psu.edu /ccma/seminar/abstracts/mov.html   (119 words)

 Particle simulation and asymptotic analysis of kinetic equations for modelling a Schottky diode   (Site not responding. Last check: 2007-11-06) Then an asymptotic analysis is performed which allows to improve the numerical solution. The asymptotic analysis is based on similar ideas as the Child-Langmuir asymptotics for vacuum diodes performed in [1]. A multidimensional extension of the asymptotic analysis is presented in [2]. mip.ups-tlse.fr /publi/rapp95/95.20.html   (233 words)

 CS195 2003S : Class 23: Asymptotic Analysis This outline was created post-course after an impromptu discussion of asymptotic analysis. Noting problems in providing a precise analysis of the running time of programs, computer scientists developed a technique which is often called asymptotic analysis. In asymptotic analysis of algorithms, one describes the general behavior of algorithms in terms of the size of input, but without delving into precise details. www.math.grin.edu /~rebelsky/Courses/CS195/2003S/Outlines/outline.23.html   (1472 words)

 Asymptotic Analysis of Algorithms As it turns out, the rules for computing and manipulating big oh expressions greatly simplify the analysis of the running time of a program when all we are interested in is its asymptotic behavior. In particular, note that all three methods of analysis are in agreement: Statements 3, 4a, and 6 execute in a constant amount of time; 4b, 4c, and 5 execute in an amount of time which is proportional to n, plus a constant. While the asymptotic analysis may be significantly easier to do, all that we get is an upper bound on the running time of the algorithm. www.pads.uwaterloo.ca /Bruno.Preiss/books/opus4/html/page70.html   (342 words)

 Asymptotic Analysis of a Learning Method in Neural Networks (ResearchIndex)   (Site not responding. Last check: 2007-11-06) Abstract: A stochastic gradient descent method applicable for training of artificial neural networks is combined with an auxiliary estimate to achieve global convergence of the recursion. Using learning rates converging slower to zero than 1=n and averaging the trajectories yield the optimal convergence rate of 1= p n and the optimal asymptotic variance as well. 3 Asymptotic properties of stochastic approximation with const.. citeseer.csail.mit.edu /400859.html   (434 words)

 Asymptotic analysis for the diffraction of sound by closely spaced and lightly loaded semi-infinite flexible surfaces ... Asymptotic analysis for the diffraction of sound by closely spaced and lightly loaded semi-infinite flexible surfaces -- Leppington and Papanikolaou 53 (2): 263 -- The Quarterly Journal of Mechanics and Applied Mathematics Asymptotic analysis for the diffraction of sound by closely spaced and lightly loaded semi-infinite flexible surfaces is to develop asymptotic solutions for the limit, of particular qjmam.oupjournals.org /cgi/content/abstract/53/2/263   (300 words)

 The high frequency asymptotic analysis of guided waves in a circular elastic annulus   (Site not responding. Last check: 2007-11-06) By using various asymptotic techniques (asymptotic reduction of the exact dispersion relation, ray methods and WKBJ analysis), we derive simple and very rapidly evaluated, asymptotically accurate dispersion relations, and reveal completely the underlying ray structures of various modes in the annulus. Comparisons of dispersion curves evaluated from the exact and asymptotic dispersion relations are presented. The typical error is less than 0.2% except for the very low frequency region; the asymptotic code is an order of magnitude faster and more stable at high frequencies. www.ma.ic.ac.uk /~rvcras/high.html   (161 words)

 The Old Joel on Software Forum - Asymptotic Analysis The intro to Data Structures course I took was taught by a PhD comp sci student who had a BS and MS in Math and to him 'real world' was quantum mechanics. I gained nothing but confusion from his algorithm analysis sections of the course. Not only does it have a good paragraph on Asymptotic Analysis, but also covers lots of algorythms to put it all into a practical context. discuss.fogcreek.com /joelonsoftware?cmd=show&ixPost=12803   (888 words)

 Asymptotic Analysis Asymptotic analysis is based on the idea that as the problem size grows, the complexity will eventually settle down to a simple proportionality to some known function. Besides, the bounds'' terminology is really not quite correct; it's just a handy mnemonic device for those who know what asymptotic analysis is really about. What is the asymptotic time complexity of this operation as a function of userpages.umbc.edu /~anastasi/Courses/341/Spr00/Lectures/Asymptotic/asymptotic/asymptotic.html   (1442 words)

 James Allen Fill (Jim Fill)   (Site not responding. Last check: 2007-11-06) Talk entitled "Combinatorial/probabilistic analysis of a class of search-tree functionals"; presented at 2001 annual IMS meeting in Atlanta, GA, August 5, 2001, session on "Combinatorial aspects of probability". Asymptotic Analysis via Mellin Transforms for Small Deviations in $L^2$-norm of Integrated Brownian Sheets. The Number of Bit Comparisons Used by Quicksort: An Average-case Analysis. www.mts.jhu.edu /~fill   (774 words)

 Solid and Structural Mechanics Books-Lewinski   (Site not responding. Last check: 2007-11-06) The results concerning the averaging problems in the linear and nonlinear shell models are also given. A unified approach to the problems is based on variational and asymptotic methods, including the methods of variational inequalities as well as homogenization techniques. A significant part of the book deals with problems important for engineering practice, such as: statical analysis of nonhomogeneous plates and shells. www.solid.ikp.liu.se /solidbook/lewi.html   (155 words)

 Intro to Asymptotic Analysis Introduce asymptotic analysis by looking at some O(n For each sorting function, we pass an array (elements of type Etype) of size N + 1, with data elements in positions 1... Asymptotic analysis is concerned with relative rates of growth. www.csee.umbc.edu /courses/undergraduate/341/fall98/frey/ClassNotes/Class7/analysis.html   (858 words)

 Talk Abstract: Renormalization Group Approach to Global Asymptotic Analysis   (Site not responding. Last check: 2007-11-06) Renormalization and the renormalization group (RG) were originally developed by physicists attempting to understand the divergent terms in perturbation theory and the short distance behaviour of quantum electrodynamics. During the last few years, these methods have been used to study the divergent terms in perturbation theory and the long time behaviour of a variety of partial differential equations. Problems studied include similarity solutions, especially intermediate asymptotics of the second kind (Barenblatt classification), and travelling waves. www.ima.umn.edu /dynsys/wkshp_abstracts/goldenfeld1.html   (167 words)

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