Software for Roundoff Analysis

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Software for Roundoff Analysis

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 1 , Issue 2 (June 1975) table of contents

Pages: 108 - 128

Year of Publication: 1975

ISSN:0098-3500

Author

Webb Miller

Computer Science Department, The Pennsylvania State University, University Park, PA

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 1, Downloads (12 Months): 24, Citation Count: 8

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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	BABUSKA, I. Numerical stability m problems of hnear algebra. SIAM J. Numer. Anal. 9 (1972), 53-77
	2	BJoacK, A. Solving linear least square problems by Gram-Schmidt orthogonahzation. BIT ? (1967), 1-21.
	3	Richard P. Brent, The Parallel Evaluation of General Arithmetic Expressions, Journal of the ACM (JACM), v.21 n.2, p.201-206, April 1974 [doi>10.1145/321812.321815]
	4	P. A. Businger, Algorithm 253 [F2]: eigenvalues of real symmetric matrix by the QR method, Communications of the ACM, v.8 n.4, p.217-218, April 1965 [doi>10.1145/363831.364858]
	5	Bernard Elspas , Karl N. Levitt , Richard J. Waldinger , Abraham Waksman, An Assessment of Techniques for Proving Program Correctness, ACM Computing Surveys (CSUR), v.4 n.2, p.97-147, June 1972 [doi>10.1145/356599.356602]
	6	C. T. Fike, Methods of evaluating polynomial approximations in function evaluation routines, Communications of the ACM, v.10 n.3, p.175-178, March 1967 [doi>10.1145/363162.363200]
	7	HART. J., et al. Computer A pproz~matTons. Wiley, New York, 1968.
	8	T. E. Hull , W. H. Enright , A. E. Sedgwick, The correctness of numerical algorithms, Proceedings of ACM conference on Proving assertions about programs, p.66-73, January 06-07, 1972, Las Cruces, New Mexico, United States
	9	William Kahan , James M. Varah, Two working algorithms for the eigenvalues of a symmetric tridiagonal matrix, Stanford University, Stanford, CA, 1966
	10	KAHAN W One numerical analyst's experience with one symbol manipulator SIAM Rev 16 (1974). 129
	11	MILLER, W Automatic a prori roundoff analysis Computing 10 (1972), 213-219.
	12	MILLER W Remarks on the complexity to round off analysis Computing 12 (1974), 149-161.
	13	MlLLER, W Numerical heuristics in COmputer-aided roundoff analysis IBM Tech. Rep. RC4332, May 2, 1973
	14	MILLER, WNumerwal search for ill-condition IBM Tech Rep RC4516, 1973.
	15	Webb Miller, Computer Search for Numerical Instability, Journal of the ACM (JACM), v.22 n.4, p.512-521, Oct. 1975 [doi>10.1145/321906.321916]
	16	hloolCE. R Internal Analysis. Prentice-Hall, Englewood Cliffs, N J, 1966
	17	OICTEC, A, J , AND KAISER, H The LLT and QR methods for symmetric trldmgonal matrices Compeller J. 6 (1963), 99-101
	18	REINSCH, C .~ stable, rational QR algorithm for the computation of the elgenvalues of an Hermltlan, trldmgonal matrix Math Compulat~on 25 (1971), 59t-597
	19	RICE. j On the conditionmg of polynomial and ratmnal forms N~tmer. 3Iath 7 (1965), 426-435
	20	RICE. J Experm~ents on Gram-Schmldt orthogonallzatmn Math Computatwn 20 (1966), 325-328
	21	STEWART, G Introductwn to Matrix Comp~ttatwns. Academic Press, New York, 1973
	22	STOUTEMYER, D Automatic error analys~s using the computer symbohc manlpulatmn language, REDUCE. Submitted to a technical journal
	23	WELSCH, J. Certfficatmn of Algorithm 253. Comm. ACM 10 (1967), 367
	24	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994
	25	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988
	26	WILKINSON, J Modern error analysis SIAM Rev 13 (1971), 548-568

CITED BY 8

	John Larson , Ahmed Sameh, Efficient Calculation of the Effects of Roundoff Errors, ACM Transactions on Mathematical Software (TOMS), v.4 n.3, p.228-236, Sept. 1978
	John L. Larson , Mary E. Pasternak , John A. Wisniewski, Algorithm 594: Software for Relative Error Analysis, ACM Transactions on Mathematical Software (TOMS), v.9 n.1, p.125-130, March 1983
	Webb Miller , David Spooner, Software for roundoff analysis, II, ACM Transactions on Mathematical Software (TOMS), v.4 n.4, p.369-387, December 1978
	Webb Miller, Computer Search for Numerical Instability, Journal of the ACM (JACM), v.22 n.4, p.512-521, Oct. 1975
	Esko Ukkonen, On the calculation of the effects of roundoff errors, ACM Transactions on Mathematical Software (TOMS), v.7 n.3, p.259-271, Sept. 1981
	David R. Stoutemyer, Automatic Error Analysis Using Computer Algebraic Manipulation, ACM Transactions on Mathematical Software (TOMS), v.3 n.1, p.26-43, March 1977
	J. H. J. Molenkamp , V. V. Goldman , J. A. van Hulzen, An improved approach to automatic error cumulation control, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.414-418, July 15-17, 1991, Bonn, West Germany
	W. J. Cody, Software basics for computational mathematics, ACM SIGNUM Newsletter, v.15 n.2, p.18-29, June 1980