Faster exponentials of power series
David Harvey

TL;DR
This paper introduces a more efficient algorithm for computing the exponential of a power series, reducing the computational complexity compared to previous methods.
Contribution
The paper presents a novel algorithm that computes exp(f) with lower asymptotic cost, improving the efficiency of power series exponential calculations.
Findings
Reduces the complexity constant from approximately 2.333 to 2.1666.
Provides an asymptotic complexity improvement for power series exponentials.
Enhances computational efficiency in symbolic and numerical analysis involving power series.
Abstract
We describe a new algorithm for computing exp(f) where f is a power series in C[[x]]. If M(n) denotes the cost of multiplying polynomials of degree n, the new algorithm costs (2.1666... + o(1)) M(n) to compute exp(f) to order n. This improves on the previous best result, namely (2.333... + o(1)) M(n).
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · Numerical Methods and Algorithms
