Abstract
Rump published an example (Algorithms for Verified Inclusions: Theory and Practice, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computing, Academic Press, Boston, 1988, pp. 109–126) in which numerical evaluation of an expression gave a misleading result, even though use of increasing arithmetic precision suggested reliable computation. This oft-cited example happens not to be reproducible on many modern computers. The expression is rewritten so that Rump's result is reproducible using IEEE 754 arithmetic.
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References
Cuyt A., Verdonk, B., Becuwe S., and Kuterna, P.: A Remarkable Example of Catastrophic Cancellation Unraveled, Computing 66 (2001), pp. 309–320.
Forte TM Developer 6 Fortran 95 Update 2, Sun Microsystems, 2001.
Hansen, E. R.: Global Optimization Using Interval Analysis, Marcel Dekker, New York, 1992.
Rump, S.M.: Algorithms for Verified Inclusions: Theory and Practiceq, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computing, chapter 1, Computer Arithmetic and Mathematical Software, Academic Press, Boston, 1988, pp. 109–126.
Walster, G. W.: Interval Arithmetic Programming Reference: Forte TM WorkShop 6 Update 2 Fortran 95, Sun Microsystems, 2001.
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Loh, E., Walster, G.W. Rump's Example Revisited. Reliable Computing 8, 245–248 (2002). https://doi.org/10.1023/A:1015569431383
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DOI: https://doi.org/10.1023/A:1015569431383