A Haskell tutorial for deriving infinite derivative chains and power series through lazy corecursion, including composition, reversion, and a Stirling-series example.
A fast algorithm for reversion of power series
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abstract
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.
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Corecursive Coding of High Computational Derivatives and Power Series
A Haskell tutorial for deriving infinite derivative chains and power series through lazy corecursion, including composition, reversion, and a Stirling-series example.