Algorithms for Solving Linear Recurrence Equations

求解线性递推方程的算法

• 批准号: 9805983
• 负责人: Mark van Hoeij
• 金额: $ 4.18万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-15 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805983&HistoricalAwards=false
• 关键词: Algorithms; Solving; Linear; Recurrence; Equations

9805983van HoeijDifference equations (i.e. recurrence equations) have a number of properties in common with differential equations. The PI recently introduced the notion of finite singularities of difference equations. With this notion, more methods for differential equations can now be applied to difference equations, and this leads to new algorithms. In particular, the PI intends to implement a new efficient algorithm for computing hypergeometric solutions of recurrence equations. These algorithms have several applications, such as finding and proving formulas, or solving certain linear differential equations.

9805983van hoeijdifference方程（即复发方程）具有许多与微分方程的共同属性。 PI最近引入了差异方程式有限奇异性的概念。 有了这个概念，现在可以将更多的微分方程方法应用于差方程，这导致了新的算法。 特别是，PI打算实现一种新的有效算法来计算复发方程的高几幅解决方案。 这些算法具有多种应用，例如查找和证明公式或求解某些线性微分方程。