Extrapolation methods and sequence transformations for computing slowly convergent integrals

用于计算缓慢收敛积分的外推方法和序列变换

• 批准号: 250223-2011
• 负责人: Safouhi, Hassan
• 金额: $ 1.09万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=479526
• 关键词: Extrapolation; methods; sequence; transformations; computing

It is well known that in applied mathematics and in the numerical treatment of scientific and engineering problems, slowly convergent integrals and series occur very frequently. They are produced by approximation procedures depending on a parameter, perturbation techniques and reliable evaluation of functions that are defined by integrals. These slowly convergent integrals and series present severe numerical and computational difficulties. Traditional quadrature rules and summation techniques fail to provide accurate approximations to these integrals and series. An effective remedy for these problems is to use extrapolation methods and convergence acceleration. These methods have proved very useful for improving convergence of infinite series and infinite-range integrals but many challenges occur when dealing with complicated integrals.

众所周知，在应用数学和科学与工程问题的数值处理中，经常会出现慢收敛的积分和级数。它们是由近似程序，取决于一个参数，扰动技术和可靠的评估功能，定义的积分。这些缓慢收敛的积分和级数提出了严重的数值和计算困难。传统的求积法则和求和技术不能提供这些积分和级数的精确近似。解决这些问题的有效方法是使用外推法和加速收敛。这些方法对于提高无穷级数和无穷范围积分的收敛性是非常有用的，但是在处理复杂的积分时会遇到许多挑战。