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 Hoeij差分方程（即递归方程）与微分方程有许多共同的性质。 PI最近引入了差分方程有限奇点的概念。 有了这个概念，更多的微分方程的方法现在可以应用于差分方程，这导致了新的算法。 特别是，PI打算实现一个新的高效算法，用于计算递归方程的超几何解。 这些算法有几个应用，如发现和证明公式，或解决某些线性微分方程。