A precise numerical analysis program

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A precise numerical analysis program

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Communications of the ACM archive
Volume 17 , Issue 9 (September 1974) table of contents

Pages: 509 - 513

Year of Publication: 1974

ISSN:0001-0782

Author

Oliver Aberth

Texas A&M Univ., College Station

Publisher

ACM New York, NY, USA

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ABSTRACT

A description is given of a program for computing the solution to a small number of standard numerical analysis problems to any specified accuracy, up to a limit of 2000 correct decimal places. Each computed number is bounded in an interval with a multiple precision midpoint. Arithmetic operations involving these numbers are executed according to interval arithmetic concepts, with non-significant digits automatically discarded. Details are supplied of problem specification and problem computation.

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	Oliver Aberth, Analysis in the Computable Number Field, Journal of the ACM (JACM), v.15 n.2, p.275-299, April 1968 [doi>10.1145/321450.321460]
	2	Aberth, O. The concept of effective method applied to computational problems of linear algebra. J. Comput. Syst. Sci. 5 (1971), 17-25.
	3	Bruce A. Chartres, Automatic Controlled Precision Calculations, Journal of the ACM (JACM), v.13 n.3, p.386-403, July 1966 [doi>10.1145/321341.321348]
	4	Dekker, T.J. Finding a zero by means of successive linear interpolation. In Constructive Aspects of the Fundamental Theorem of Algebra. Wiley-Interscience, New York, 1969, pp. 37-61.
	5	Fox. L. An Introduction to Numerical Linear Algebra. Oxford Univ. Press, New York, 1965.
	6	Hill, I.D. Procedures for the basic arithmetical operations in multiple-length working. Computer J. 11 (1968), 232-235.
	7	Moore, R.E. htterval Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1966.
	8	David A. Pope , Marvin L. Stein, Multiple precision arithmetic, Communications of the ACM, v.3 n.12, p.652-654, Dec. 1960 [doi>10.1145/367487.367499]
	9	Paul L. Richman, Automatic error analysis for determining precision, Communications of the ACM, v.15 n.9, p.813-817, Sept. 1972 [doi>10.1145/361573.361581]
	10	Richman, P.L. Private communication, 1969.
	11	Marvin L. Stein, Divide-and-correct methods for multiple precision division, Communications of the ACM, v.7 n.8, p.472-474, Aug. 1964 [doi>10.1145/355586.364796]

CITED BY 3

	Richard P. Brent, A Fortran Multiple-Precision Arithmetic Package, ACM Transactions on Mathematical Software (TOMS), v.4 n.1, p.57-70, March 1978
	Vernon A. Lee, Jr. , Hans-J. Boehm, Optimizing programs over the constructive reals, ACM SIGPLAN Notices, v.25 n.6, p.102-111, Jun. 1990
	Branimir Lambov, RealLib: An efficient implementation of exact real arithmetic, Mathematical Structures in Computer Science, v.17 n.1, p.81-98, February 2007