Separable asymptotic cost of evaluating elementary functions

The computational cost, in the bit model of computation, of the evaluation of a real function in a point is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on also when approaches a critical point for the function f. We inve...

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Bibliographic Details
Published in:Numerical algorithms Vol. 24; no. 3; pp. 255 - 274
Main Authors: Favati, P., Lotti, G., Menchi, O., Romani, F.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.08.2000
Subjects:
Asymptotic properties
Computing costs
Critical point
Upper bounds
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The computational cost, in the bit model of computation, of the evaluation of a real function in a point is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on also when 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 , that is as products of two functions, each of one variable. We examine in particular the case of elementary functions.
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ISSN:1017-1398
1572-9265
DOI:10.1023/A:1019101512077