Fast high-precision computation of complex square roots

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Fast high-precision computation of complex square roots

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents

Zurich, Switzerland

Pages: 142 - 149

Year of Publication: 1996

ISBN:0-89791-796-0

Author

Timm Ahrendt

Institut fü Informatik II, University of Bonn, Römerstr, 164, D - 53117 Bonn, Germany

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 8, Downloads (12 Months): 14, Citation Count: 1

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	AHLFORS, L. V. Complex Analysis. McGraw-Hill, New York, 1953.
	2	AHRENDT~ T. Schnelle Berechnungen der komplexen Quadratwurzel auf hohe Genauigkeit. Diploma thesis, University of Bonn, Jan. 1995.
	3	ALT, H. Algorithms for square root extraction. Report A 77-12, Fachbereich Angewandte Mathematik und Informatik, Saarbrficken, 1977.
	4	BAILEY, D. H. A portable high performance multiprecision package. RNR Technical Report RNR-90-022, NAS Applied Research Branch, NASA Ames Research Center, Moffett Filed, CA 94035, May 1993.
	5	BRENT, R. P. Multiple-precision zero-finding methods and the complexity of elementary function evaluation. In Analytic Computatwnal Complexity, J. F. Traub, Ed. Academic Press, New York, 1976, pp. 151-176.
	6	Alan H. Karp , Peter Markstein, High-precision division and square root, ACM Transactions on Mathematical Software (TOMS), v.23 n.4, p.561-589, Dec. 1997 [doi>10.1145/279232.279237]
	7	LICKTEIG, T., AND WERTHER, K. How to compute a complex square root optimally? To appear in Computational Complexity, 1994.
	8	PERRON, O. Die Lehre yon den Kettenbriichen, 3rd ed., vol. 1. Teubner, Stuttgart, 1954.
	9	RAMAMOORTHY, C. V., GOODMAN, J. R., AND KIM, K. H. Some properties of iterative square-rooting met,hods using high-speed multiplication. IEEE Trans. Cornput. 21, 8 (1972), 837-847.
	10	SCHONHAGE, A. Private communication. 1994.
	11	SCH(~NHAGE, A., GROTEFELD, A. F. W., AND VET- TER, E. Fast Algorithms: A Multitape Taring Machine Implementation. B.I. Wissenschaftsverlag, Mannheim, 1994.
	12	Stephen Wolfram, Mathematica: a system for doing mathematics by computer (2nd ed.), Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1991