Rump's Example Revisited
Tóm tắt
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.
Tài liệu tham khảo
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.