• 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