Stable computation of the complex roots of unity

Shows 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 mod...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	IEEE transactions on signal processing 1995-07, Vol.43 (7), p.1709-1711
1. Verfasser:	Tate, S.R.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Computer science Difference equations Exact sciences and technology Fast Fourier transforms Information, signal and communications theory Mathematical methods NASA Subcontracting Telecommunications and information theory
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Shows 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. The author gives alternative formulas, which are shown to be superior both by analysis and experiment.< >
ISSN:	1053-587X 1941-0476
DOI:	10.1109/78.398732