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引用次数: 6
摘要
提出了一种具有有理函数系数的Fuchsian常微分算子的符号-数值Las Vegas算法。新算法结合了van Hoeij的“局部到全局”方法和van der Hoeven提出的“解析”方法的思想。在局部到全局方法成功的“简单”情况下，它本质上简化为前者，在“最难”情况下，它简化为后者的优化变体，同时比两者更有效地处理中间情况。
Symbolic-Numeric Factorization of Differential Operators
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.
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