科研之友
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摘要
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires O(n(1/2)(M(n) + MM(n(1/2)))) operations where M(n) and MM(n) are the costs of polynomial and matrix multiplication, respectively. This matches the asymptotic complexity of an algorithm of Brent and Kung, but we achieve a constant factor speedup whose magnitude depends on the polynomial and matrix multiplication algorithms used. Benchmarks confirm that the algorithm performs well in practice.
- 出版日期2015-1
