Stable Computation of the Complex Roots of Unity

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Stephen R. Tate, Professor and Department Head (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: In this correspondence, 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.

Additional Information

Publication
IEEE Transactions on Signal Processing, Vol. 43, No. 7, 1995, pp. 1709–1711.
Language: English
Date: 1995
Keywords
Computation theory, Formula, Stability