A simple and fast algorithm for computing exponentials of power series

@article{Bostan2009ASA,
  title={A simple and fast algorithm for computing exponentials of power series},
  author={Alin Bostan and {\'E}ric Schost},
  journal={ArXiv},
  year={2009},
  volume={abs/1301.5804}
}

Figures from this paper

Fast algorithms for elementary operations on complex power series
Abstract It is shown that the inversion of a complex-valued power series can be realised asymptotically with complexity of 5/4 multiplications (if we compare the upper bounds). It is shown that the
Homotopy techniques for multiplication modulo triangular sets ( Spine
TLDR
This thesis obtains a quasi-linear time complexity for substantial families of examples, for which no such result was known before, and proposes an algorithm that relies on homotopy and fast evaluation-interpolation techniques.
Solving composite sum of powers via Padé approximation and orthogonal polynomials with application to optimal PWM problem
  • P. Kujan
  • Mathematics, Computer Science
    Appl. Math. Comput.
  • 2014
Complete Fast Analytical Solution of the Optimal Odd Single-Phase Multilevel Problem
TLDR
A new general modulation strategy for ML inverters is introduced, which takes an analytic form and is very fast, with a complexity of only O(n log2 n) arithmetic operations, where n is the number of controlled harmonics.
Counting Matrices that are Squares
On the math-fun mailing list (7 May 2013), Neil Sloane asked to calculate the number of $n \times n$ matrices with entries in $\{0,1\}$ which are squares of other such matrices. In this paper we
3 Matrices and Their Conjugacy Classes
  • 2016
Single-phase optimal Odd PWM problem
TLDR
An exact and fast algorithm with the complexity of only O(n log2 n) arithmetic operations is introduced for computation of optimal switching angles of a odd PWM waveform for generating general odd symmetric waveforms.

References

SHOWING 1-10 OF 14 REFERENCES
The truncated fourier transform and applications
TLDR
A truncated version of the classical Fast Fourier Transform that has the nice property of eliminating the "jumps" in the complexity at powers of two and gains a logarithmic factor with respect to the best previously known algorithms.
Newton's method and FFT trading
Fast Algorithms for Manipulating Formal Power Series
TLDR
This paper shows that the composition and reversion problems are equivalent (up to constant factors), and gives algorithms which require only order (n log n) ~/2 operations in many cases of practical importance.
Variations on computing reciprocals of power series
Modern computer algebra
TLDR
This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
Modern Computer Algebra
TLDR
This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
Relax, but Don't be Too Lazy
TLDR
This paper surveys several classical and new zealous algorithms for manipulating formal power series, including algorithms for multiplication, division, resolution of differential equations, composition and reversion, and gives various relaxed algorithms for these operations.
Removing redundancy in high-precision
  • Newton iteration,
  • 2004
REMOVING REDUNDANCY IN HIGH-PRECISION NEWTON ITERATION
This paper presents new algorithms for several high-precision operations in the power series ring C[[x]]. Compared to computing n coefficients of a product in C[[x]], computing n coefficients of a
...
1
2
...