Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: Miller's recurrence algorithm for tabulating the subdominant solution of a second-order difference equation is modified so as to take the asymptotic behaviour of the solution into account as discussed by the authors.
Abstract: Miller's recurrence algorithm for tabulating the subdominant solution of a second-order difference equation is modified so as to take the asymptotic behaviour of the solution into account. The asymptotic solutions of various types of equations are listed, and a method is given for estimating the error in the tabulated solution.
17 citations
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TL;DR: In this article, the spectral mapping theorem was used to derive the spectrum of the strongly continuous semigroup of the forced elongation in the isothermal regime, and the spectral properties of the eigenvalues were determined by solving a characteristic integral equation in the complex plane.
17 citations
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TL;DR: In this paper, the asymptotic behavior of recursive estimation procedures is studied and the results of the analysis can be used to determine the form of the recursive procedure which is expected to have the same properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation.
Abstract: This paper is concerned with the asymptotic behaviour of estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The results of the paper can be used to determine the form of the recursive procedure which is expected to have the same asymptotic properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation. Several examples are given to illustrate the theory, including an application to estimation of parameters in exponential families of Markov processes.
17 citations
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TL;DR: This paper presents a general scheme for the design of such ''asymptotic extrapolation algorithms'' using discrete differentiation and techniques from automatic asymptotics, to approximate the coefficients in the expansion with high accuracy.
17 citations