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Numerically stable forms

  1. Aug 22, 2004 #1

    I have an assignment lying around, in which I have to find numerically stable forms of some expressions. A few still elude me, so I was wondering if someone might have a suggestion.


    This has large rounding errors if x is close to 1

    sinh (x) - tanh (x)

    Large errors for x close to 0


    No idea...
    Last edited: Aug 22, 2004
  2. jcsd
  3. Aug 22, 2004 #2


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  4. Aug 22, 2004 #3
    Yes, a Taylor expansion does seem obvious; but alas, the'yre asking analytical forms...
  5. Aug 23, 2004 #4


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    Use a similar trick for 1, by noting [tex]sinh(y)=\frac{e^{y}-e^{-y}}{2}[/tex]
    Last edited: Aug 23, 2004
  6. Aug 23, 2004 #5
    Thanks! This is just what I needed!
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