渐近级数的自相似逼近外推与内插
Extrapolation and interpolation of asymptotic series by self-similar approximants
摘要：
考虑渐近级数的外推与内插问题。提出了几种新的改进自相似逼近精度的方法。当人们有兴趣找到一个强相互作用系统的状态方程时，典型的化学物理的例子说明了这些方法。特别注意研究波动流体膜的基本性质。结果表明，这些性质可以很好地描述的自相似逼近的方法。为此目的，该方法已被推广，以提供准确的预测在无穷远的功能，其行为是已知的，只有在该地区的变量接近零。对脉动流体膜的计算结果与已知的数值结果吻合较好。
英文摘要：
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical physics, when one is interested in finding the equation of state for a strongly interacting system. A special attention is payed to the study of the basic properties of fluctuating fluid membranes. It is shown that these properties can be well described by means of the method of self-similar approximants. For this purpose, the method has been generalized in order to give accurate predictions at infinity for a function, whose behavior is known only at the region of its variable close to zero. The obtained results for fluctuating fluid membranes are in good agreement with the known numerical data.
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