English

A note on the fast power series' exponential

Data Structures and Algorithms 2012-03-20 v1

Abstract

It is shown that the exponential of a complex power series up to order n can be implemented via (23/12+o(1))M(n) binary arithmetic operations over complex field, where M(n) stands for the (smoothed) complexity of multiplication of polynomials of degree <n in FFT-model. Yet, it is shown how to raise a power series to a constant power with the complexity (27/8+o(1))M(n).

Keywords

Cite

@article{arxiv.1203.3883,
  title  = {A note on the fast power series' exponential},
  author = {Igor S. Sergeev},
  journal= {arXiv preprint arXiv:1203.3883},
  year   = {2012}
}

Comments

7 pages, in English; 7 pages, in Russian

R2 v1 2026-06-21T20:35:39.424Z