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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304 citations
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300 citations
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01 Jan 1973
TL;DR: In this paper, the authors discuss the asymptotic behavior of the solution when the parameter tends to a limiting value of its range, where the solution is obtained first in a more or less explicit form, and is then simplified by the appropriate asymPT expansions when the parameters tend to one or both limiting values of its interval.
Abstract: Asymptotic methods play an important role in all branches of applied mathematics in the evaluation of the solutions of problems depending on a parameter with a certain range. Usually the solution is obtained first in a more or less explicit form, and is then simplified by the appropriate asymptotic expansions when the parameter tends to one or both limiting values of its interval. On the other hand, in elasticity one often encounters problems for which no explicit solution is available for arbitrary values of the parameter. Numerical techniques may enable us to obtain accurate numerical solutions for specific values of the parameter. Such numerical methods, however, are often less convenient to discuss the asymptotic behaviour of the solution when the parameter tends to a limiting value of its range.
296 citations
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TL;DR: In this article, the asymptotic consistency of cross-validatory assessment and the efficiency of crossvalidatory choice is investigated both in some generality and also in the context of particular applications.
Abstract: SUMMARY The asymptotic consistency of cross-validatory assessment and the asymptotic efficiency of cross-validatory choice is investigated both in some generality and also in the context of particular applications.
289 citations