Iterative Refinement in Floating Point

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Iterative Refinement in Floating Point

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Journal of the ACM (JACM) archive
Volume 14 , Issue 2 (April 1967) table of contents

Pages: 316 - 321

Year of Publication: 1967

ISSN:0004-5411

Author

Cleve B. Moler

Department of Mathematics, University of Michigan, Ann Arbor, Michigan and Swiss Federal Institute of Technology, Zurich, Switzerland

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 16, Downloads (12 Months): 91, Citation Count: 8

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ABSTRACT

Iterative refinement reduces the roundoff errors in the computed solution to a system of linear equations. Only one step requires higher precision arithmetic. If sufficiently high precision is used, the final result is shown to be very accurate.

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	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994
	2	KAXHAN, W. Writeups of library tape subroutines LEQU, LEQUN, FLEQU, CLEQU nd DLEQU. Inst. Computer Sci., U. of Toronto, 1965 (various months).
	3	MOLER, C. SOLVE, Accurate simultaneous linear equation solver with iterative improvement. SHARE Distribution No. 3194, 1964.
	4	William Marshall McKeeman, Algorithm 135: Crout with equilibration and iteration, Communications of the ACM, v.5 n.11, p.553-555, Nov. 1962 [doi>10.1145/368996.369009]
	5	MARTIN, R. S., PERES, G., AND WILKINSON, J .H . Iterative refinement of the solution of positive definite system of equations. Numer. Math. 8 (1966), 203-216.
	6	BOWDLER, H. J., MARTIN, R. S., PETERS, G., AND WILKINSON, J. g . Solution of real nd complex systems of equations. Numer. Math. 8 (1966), 217-234.

CITED BY 8

	Edward F. Puccinelli, Improving iterative improvement, Proceedings of the 1971 26th annual conference, p.736-744, January 1971
	Nai-kuan Tsao, Some a Posteriori Error Bounds in Floating-Point Computations, Journal of the ACM (JACM), v.21 n.1, p.6-17, Jan. 1974
	Richard H. Bartels , Gene H. Golub, Numerical Analysis: Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations, Communications of the ACM, v.11 n.6, p.401-406, June 1968
	James Demmel , Yozo Hida , William Kahan , Xiaoye S. Li , Sonil Mukherjee , E. Jason Riedy, Error bounds from extra-precise iterative refinement, ACM Transactions on Mathematical Software (TOMS), v.32 n.2, p.325-351, June 2006
	Julie Langou , Julien Langou , Piotr Luszczek , Jakub Kurzak , Alfredo Buttari , Jack Dongarra, Tools and techniques for performance---Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems), Proceedings of the 2006 ACM/IEEE conference on Supercomputing, November 11-17, 2006, Tampa, Florida
	Alfredo Buttari , Jack Dongarra , Jakub Kurzak , Piotr Luszczek , Stanimir Tomov, Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy, ACM Transactions on Mathematical Software (TOMS), v.34 n.4, p.1-22, July 2008
	Alfredo Buttari , Jack Dongarra , Julie Langou , Julien Langou , Piotr Luszczek , Jakub Kurzak, Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems, International Journal of High Performance Computing Applications, v.21 n.4, p.457-466, November 2007
	P. Alonso , J. Delgado , R. Gallego , J. M. Pena, Iterative refinement for Neville elimination, International Journal of Computer Mathematics, v.86 n.2, p.341-353, February 2009