A simple and fast online power series multiplication and its analysis

This paper focuses on online (or relaxed) algorithms for the multiplication of power series over a field and their complexity analysis. We propose a new online algorithm for the multiplication using middle and short products of polynomials as building blocks, and we give the first precise analysis of the arithmetic complexity of various online multiplications. Our algorithm is faster than Fischer and Stockmeyer's by a constant factor; this is confirmed by experimental results.