1
$\begingroup$

I'm approximating $\pi$ using a series in MATLAB. I can approximate to within a relative error of $3\times 10^{-10}$ of MATLAB's built-in value. How would I choose a sensible tolerance for my approximation? Would it possibly relate to machine epsilon?

  • 0
    Which series? ${}$2011-10-05
  • 0
    $ 1 - 1/3 + 1/5 - 1/7 + ...$2011-10-05
  • 0
    Yeow, that one's quite slow to converge. Do you really need to use that series?2011-10-05
  • 1
    I'm afraid I do. I want to compare it to Matlab's built-in value for pi for a varying number of terms in this series.2011-10-05
  • 1
    The usual criterion is to stop when the $k$-th term is less than the current partial sum times `eps`.2011-10-05
  • 0
    Sounds reasonable. I am new to numerical methods. Thanks.2011-10-05
  • 1
    Hmm, change that to "absolute value of the $k$-th term"...2011-10-05
  • 0
    Ok, cool. I'll try that.2011-10-05

1 Answers 1

1

"The usual criterion is to stop when the absolute value of the k-th term is less than the current partial sum times eps"

Thanks to @J.M.