发表机构
School of Mathematical Sciences, Tel-Aviv University（特拉维夫大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展Levin方法至一维和多维无穷振荡级数求和，通过将求和问题转化为函数方程求解，尤其适用于现有方法受限的多维情形。
AI 中文摘要
Levin方法将高度振荡积分的计算转化为一个关于缓慢变化辅助函数的一阶线性常微分方程的求解。该常微分方程通常通过配点法近似求解，随后从辅助函数在端点处的值恢复积分值。本文工作为Levin方法发展了一种新的扩展，用于一维和多维无穷振荡级数的求和。求和问题被转化为一个涉及未知函数变换自变量的函数方程的求解。所得到的方法在多维情形下尤其具有吸引力，因为现有数值方法在该领域的适用范围相对有限。
英文摘要
The Levin method transforms the evaluation of a highly oscillatory integral into the solution of a first-order linear ODE for a slowly varying auxiliary function. This ODE is typically approximated by collocation, after which the integral value is recovered from the auxiliary function at the endpoints. The present work develops a new extension of the Levin method for the summation of one-dimensional and multidimensional infinite oscillatory series. The summation problem is transformed into the solution of a functional equation involving transformed arguments of the unknown function. The resulting approach is particularly attractive in the multidimensional setting, where the range of existing numerical methods is relatively limited.
Comments17 pages
