Precise evaluation of polynomials in several variables. (English) Zbl 0661.65017
Scientific computation with automatic result verification, Proc. Conf. Comput. Arith. Sci. Comput., Karlsruhe/FRG 1987, Comput. Suppl. 6, 139-148 (1988).
[For the entire collection see Zbl 0646.00013.]
An algorithm is presented which computes the values of polynomials in several variables with high accuracy when the computation is done in a floating-point system using a precise scalar product and directed rounding. Furthermore the value of the polynomial is enclosed in narrow bounds. Numerical examples demonstrate the high precision of the results and show that traditional algorithms can fail completely for this problem. The algorithm presented here is a generalization of Böhm’s algorithm for one-dimensional polynomials.
An algorithm is presented which computes the values of polynomials in several variables with high accuracy when the computation is done in a floating-point system using a precise scalar product and directed rounding. Furthermore the value of the polynomial is enclosed in narrow bounds. Numerical examples demonstrate the high precision of the results and show that traditional algorithms can fail completely for this problem. The algorithm presented here is a generalization of Böhm’s algorithm for one-dimensional polynomials.
Reviewer: Wang Xinghua
MSC:
| 65D20 | Computation of special functions and constants, construction of tables |
| 65G30 | Interval and finite arithmetic |
