A fast algorithm for reversion of power series

@article{Johansson2015AFA,
  title={A fast algorithm for reversion of power series},
  author={F. Johansson},
  journal={Math. Comput.},
  year={2015},
  volume={84},
  pages={475-484}
}
  • F. Johansson
  • Published 2015
  • Computer Science, Mathematics
  • Math. Comput.
  • We give an algorithm for reversion of formal power series, based on an efficient way to evaluate 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 an algorithm of Brent and Kung, but we achieve a constant factor speedup whose magnitude depends on the polynomial and matrix multiplication algo- rithms used. Benchmarks confirm that the algorithm performs… CONTINUE READING
    Fast multivariate multi-point evaluation revisited
    • ORIS VAN DER, OEVEN
    • 2018
    Fast multivariate multi-point evaluation revisited
    8
    Modular composition via factorization
    • ORIS VAN DER, OEVEN, RÉGOIRE, ECERF
    • 2018
    Modular composition via factorization
    10
    Faster Arbitrary-Precision Dot Product and Matrix Multiplication
    2
    Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
    56
    Learning in Integer Latent Variable Models with Nested Automatic Differentiation
    1
    On Random Sampling for Compliance Monitoring in Opportunistic Spectrum Access Networks
    1

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 31 REFERENCES
    Fast Algorithms for Manipulating Formal Power Series
    237
    Fast composition of numeric power series ∗
    13
    Power series composition and change of basis
    22
    Faster algorithms for the square root and reciprocal of power series
    16
    REMOVING REDUNDANCY IN HIGH-PRECISION NEWTON ITERATION
    • DANIEL J. BERNSTEINf
    • 2004
    22
    Fast Rectangular Matrix Multiplication and Applications
    223
    Composing Power Series Over a Finite Ring in Essentially Linear Time
    24
    On the complexity of matrix multiplication
    204
    Relax, but Don't be Too Lazy
    119