论文标题
差分运算符的符号数分解
Symbolic-Numeric Factorization of Differential Operators
论文作者
论文摘要
我们提出了一种符号数字拉斯维加斯算法，用于考虑具有合理功能系数的紫红色的普通差分运算符。新算法结合了van Hoeij的“本地到全球”方法的思想和van der Hoeven提出的“分析”方法。从本质上，它减少了“易于”局部到全球方法成功的“简易”案例中的前者，而在“最难”情况下，它比后者的优化变体，同时比两者更有效地处理中间情况。
We present a symbolic-numeric Las Vegas algorithm for factoring Fuchsian ordinary differential operators with rational function coefficients. The new algorithm combines ideas of van Hoeij's "local-to-global" method and of the ''analytic'' approach proposed by van der Hoeven. It essentially reduces to the former in ''easy'' cases where the local-to-global method succeeds, and to an optimized variant of the latter in the "hardest" cases, while handling intermediate cases more efficiently than both.
