3 citations · 6 across the 4 of their papers we have counts for
5 papers
Faster algorithms for the square root and reciprocal of power series
David Harvey
We give new algorithms for the computation of square roots and reciprocals of power series in C[[x]]. If M(n) denotes the cost of multiplying polynomials of degree n, the square ro…
A cache-friendly truncated FFT
David Harvey
We describe a cache-friendly version of van der Hoeven's truncated FFT and inverse truncated FFT, focusing on the case of `large' coefficients, such as those arising in the Schonha…
A multimodular algorithm for computing Bernoulli numbers
David Harvey
We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed B(k) for k = 10^8, a new record. Our method is to compute B(k) modulo p…
Faster polynomial multiplication via multipoint Kronecker substitution
David Harvey
We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on…
Efficient computation of p-adic heights
David Harvey
We analyse and drastically improve the running time of the algorithm of Mazur, Stein and Tate for computing the canonical cyclotomic p-adic height of a point on an elliptic curve E…