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Showing papers on "Asymptotology published in 1987"


Journal ArticleDOI
TL;DR: In this article, the authors present an analysis of the asymptotic behavior of the solutions to various iterative linear least-squares methods that synthesize transfer functions from frequency-response data.
Abstract: This paper presents an analysis of the asymptotic behaviour of the solutions to various iterative linear least-squares methods that synthesize transfer functions from frequency-response data. The methods of Sanathanan and Koerner and Lawrence and Rogers are shown to possess asymptotic solutions that do not coincide with the solution to a fundamental non-linear least-squares criterion. Several methods with more appropriate asymptotic behaviour are then suggested. The analytical tools presented should allow analysis of conditions for the convergence of iterative linear least-squares methods.

75 citations


Journal ArticleDOI
TL;DR: In this article, an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode) is carried out.
Abstract: In this paper we carry out an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode). We determine the different time scales present in the equations and investigate which of them actually occur in physical situations. We derive asymptotic expansions of the solution and perform some numerical experiments.

27 citations



Book ChapterDOI
01 Jan 1987

21 citations


Journal ArticleDOI
TL;DR: In this article, a detailed asymptotic analysis of spectral methods for prototype problems is presented, and a number of surprising results are presented, including the O(N) boundedness of the eigenvalues of collocation on Legendre points.
Abstract: A detailed asymptotic analysis of spectral methods for prototype problems is presented. Asymptotic error behavior throughout the solution regime is given. A number of surprising results are presented, including theO(N) boundedness of the eigenvalues of collocation on Legendre points.

16 citations


Journal ArticleDOI
TL;DR: The Matched Asymptotic Expansion Method (MAPMEM) as discussed by the authors is one of the most well-known methods for fitting line integrals with singular kernels, but it is not well adapted to deal with Finite Part integrals.
Abstract: Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are “improper”, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.

14 citations




Journal ArticleDOI
TL;DR: The main results on the optimization of Monte Carlo algorithms based on the asymptotic solutions of the transport theory are presented in this paper, where the methods of constructing such algorithms for a number of problems in atmospheric optics are analysed.
Abstract: The main results on the optimization of Monte Carlo algorithms based on the asymptotic solutions of the transport theory are presented. The methods of constructing such algorithms for a number of problems in atmospheric optics are analysed. Approaches to optimizing the simulation of radiative transfer with non-exponential absorption are described. The algorithms are aimed at computing the transmission of IR radiation through cloud layers in the absorption bands of atmospheric gases. 1. IMPORTANCE SAMPLING In terms of the ray-optics approximation, the transfer of optic radiation in scattering and absorbing media can be described (see, for example, [9]) by an integral equation of the second kind f J /(x)= /c(x',x)/(x')dx' + iA(x) (1.1) x where /(x) is the density of collisions or scattering events for particles (light quanta) in the medium in the phase space Χ; χ and χΈΧ\ and ψ(χ) is the density of'collisions' in the source. We shall consider problems whose solutions can be reduced to estimating functional of the type J* = (/, Φ) = I /(*)#*) dx, φ(χ) > 0. (1.2) Jx It is well known (see, for example, [4]) that

3 citations


Book ChapterDOI
01 Jan 1987
TL;DR: In this paper, a definition of asymptotic expectation is given and its fundamental properties are discussed, and a detailed discussion of the fundamental properties of the definition of expectation is provided.
Abstract: In this paper a definition of asymptotic expectation is given and its fundamental properties are discussed.

3 citations


Journal ArticleDOI
TL;DR: In this article, finite sample relations among exact and asymptotic tests of non-nested linear regression models are established, and finite sample relation is established among some exact and approximate tests.

Journal ArticleDOI
TL;DR: In this article, an asymptotic expansion for solving a quasistatic thermo-elasticity problem for a slender cylindrical rod in the presence of mass forces and non-linear heat sources is constructed.

Journal ArticleDOI
TL;DR: In this article, an integral statistic for the testing of the independence of the coordinates of a two-dimensional random vector is introduced, and with its aid one computes the Bahadur exact slope of the considered sequence of statistics for close noncontinual alternatives.
Abstract: One introduces an integral statistic for the testing of the independence of the coordinates of a two-dimensional random vector. One finds the coarse asymptotic behavior of the probabilities of large deviations of this statistic and with its aid one computes the Bahadur exact slope of the considered sequence of statistics for close noncontinual alternatives. One investigates the Bahadur efficiency and the structure of the domain of the local asymptotic optimality of this sequence.




Journal ArticleDOI
TL;DR: In this article, the perturbational mapping function in Savin's form was used to solve the diffraction of the electromagnetic waves by a perfect conductor, and the general method and asymptotic formulas to solve this problem were presented.
Abstract: In this paper, the two dimentional problems of the diffraction of the electromagnetic waves by a perfect conductor are discussed by using the perturbational mapping function in Savin’s form. The general method and asymptotic formulas to solve this problem are presented. Especially, for the asymptotic solutions based on a circular cylindrical conductor, the formulas to calculate “O”—order and “I”—order asymptotic solution are given

Journal ArticleDOI
Xiuchun Li1
TL;DR: In this paper, the authors give a complete asymptotic expansion of the Jacobi functions as λ→ + ∞ for an improper integral in which the integrand is an unbounded function and contains a parameter.
Abstract: In this paper we give a complete asymptotic expansion of the Jacobi functionsφ () (t) as λ→ + ∞. The method we employed to get the complete expansion follows that of Olver in treating similar problems. By using a Gronwall-Bellman type inequality for an improper integral in which the integrand is an unbounded function and contains a parameter, we get an error bound of the asymptotic approximation which is different from that of Olver's.