DocumentCode :
1338154
Title :
Efficient computation of erfc(x) for large arguments
Author :
Tellambura, C. ; Annamalai, A.
Author_Institution :
Dept. of Comput. Sci., Monash Univ., Clayton, Vic., Australia
Volume :
48
Issue :
4
fYear :
2000
fDate :
4/1/2000 12:00:00 AM
Firstpage :
529
Lastpage :
532
Abstract :
A new, infinite series representation for the error function is developed. It is especially suitable for computing erfc(x) for large x. For instance, for any x⩾4, the error function can be evaluated with a relative error less than 10-10 by using only eight terms. Similarly, the error function can be evaluated with a relative error less than 8×10-7 for any x⩾2 using just six terms. An analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases. Comparisons with two other series are provided
Keywords :
Gaussian noise; error analysis; information theory; interference (signal); sampling methods; series (mathematics); analytical bound; efficient computation; erfc(x); error function; infinite series representation; large arguments; relative error; series truncation; undersampling; Approximation methods; Closed-form solution; Computer errors; Convergence; Error probability; Frequency; Integral equations; Random variables; Sampling methods; Tail;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/26.843116
Filename :
843116
Link To Document :
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