Abstract:We define an axiom system for rounded arithmetic to be complete if we can recover from any model of the axioms the exact algebra from whence it came. A complete set of axioms is given for rounded addition and multiplication.
- Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
- Ulrich W. Kulisch and Willard L. Miranker, Computer arithmetic in theory and practice, Computer Science and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 606741 L. B. Rall, Accurate Arithmetic for Scientific Computation, Proceedings of the 1982 Army Numerical Analysis and Computer Conference, 1982.
- J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 42 (1984), 623-635
- MSC: Primary 65G99; Secondary 03B70, 03C70, 68Q40
- DOI: https://doi.org/10.1090/S0025-5718-1984-0736458-7
- MathSciNet review: 736458