Abstract
The computational cost, in the bit model of computation, of the evaluation of a real function \(f(x)\) in a point \(x\) is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on \(x\) also when \(x\) approaches a critical point for the function f. We investigate the hypotheses under which it is possible to give upper bounds on the cost as functions of “separated variables” d and \(x\), that is as products of two functions, each of one variable. We examine in particular the case of elementary functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Aho, J. Hopcroft and J. Ullman, The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, MA, 1974).
K.E. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978).
J.M. Borwein and P.B. Borwein, Pi and the AGM (Wiley, New York, 1986).
P.R. Brent, Fast multiple-precision evaluation of elementary functions, J. ACM 23 (1976) 242-251.
P. Favati, Asymptotic bit cost of quadrature formulas obtained by variable transformation, Appl. Math. Lett. 10 (1997) 1-7.
P. Favati, G. Lotti, O. Menchi and F. Romani, Separable asymptotic cost of evaluating elementary functions, Technical Report IMC, CNR, Pisa, B4-96-10 (1996).
K. Ko, Complexity Theory of Real Functions (Birkhäuser, Boston, 1991).
Rights and permissions
About this article
Cite this article
Favati, P., Lotti, G., Menchi, O. et al. Separable asymptotic cost of evaluating elementary functions. Numerical Algorithms 24, 255–274 (2000). https://doi.org/10.1023/A:1019101512077
Issue Date:
DOI: https://doi.org/10.1023/A:1019101512077