Publication Information
S. R. Tate. Stable Computation of the Complex Roots of Unity, in IEEE Transactions on Signal Processing, Vol. 43, No. 7, 1995, pp. 1709--1711. GeometryJournal
Abstract
In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at first. In particular, the formulas given in a standard programmer’s reference book [Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable, giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both by analysis and experiment.