Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
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25 Jun 2012
TL;DR: This work gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes, and resolves the long-standing problem of devising a reliable algorithm for estimating these constants.
Abstract: This work gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for estimating these constants. A detailed error analysis illustrates the strength of our approach. (Joint with Ton Dieker, Georgia Institute of Technology)
57 citations
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TL;DR: A survey of results on the asymptotic analysis of autoresonance can be found in this article, where systems of differential equations corresponding to non-linear non-autonomous oscillators with variable excitation frequency are considered.
Abstract: In recent decades new problems have arisen in oscillation theory which are related to the investigation of a?physical phenomenon known as autoresonance. This paper presents a?survey of results on the asymptotic analysis of such problems. Systems of differential equations corresponding to non-linear non-autonomous oscillators with variable excitation frequency are considered. For their solution asymptotic formulae are constructed with respect to a?small parameter or with respect to an independent variable.
56 citations
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55 citations
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55 citations
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25 Apr 1996
TL;DR: Asymptotic expansion and linear extrapolation methods have been studied in this article for philosophy error bounds, stopping rules and monotonicity generalizations, with a focus on linear expansion.
Abstract: Part 1 Asymptotic expansion: asymptotic systems and expansions geometric asymptotic expansions logarithmic asymptotic expansions. Part 2 Linear extrapolation methods: fundamental concepts and general philosophy error bounds, stopping rules and monotonicity generalizations and final remarks.
54 citations