73 citations · 398 across the 44 of their papers we have counts for
4 papers · 1 filter
Computing with functions in spherical and polar geometries I. The sphere
Alex Townsend, Heather Wilber, Grady B. Wright
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by u…
Numerical instability of resultant methods for multidimensional rootfinding
Vanni Noferini, Alex Townsend
Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they ar…
A fast FFT-based discrete Legendre transform
Nicholas Hale, Alex Townsend
An algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast tr…
A fast analysis-based discrete Hankel transform using asymptotic expansions
Alex Townsend
A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order as well as evaluating Schlömilch and Fourier--Bessel expansions in $\m…