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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| Published in: | Numerical algorithms Vol. 24; no. 3; pp. 255 - 274 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer Nature B.V
01.08.2000
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| ISSN: | 1017-1398, 1572-9265 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Romani, F. Menchi, O. Favati, P. Lotti, G. |
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| References | P. Favati (329397_CR5) 1997; 10 A. Aho (329397_CR1) 1974 K. Ko (329397_CR7) 1991 J.M. Borwein (329397_CR3) 1986 329397_CR6 P.R. Brent (329397_CR4) 1976; 23 K.E. Atkinson (329397_CR2) 1978 |
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| SubjectTerms | Asymptotic properties Computing costs Critical point Upper bounds |
| Title | Separable asymptotic cost of evaluating elementary functions |
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