1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical Analysis, sensitivity root finding.

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]Let f(x) = x^{n} - ax^{n-1},\: and \: set\: g(x) = x^{n} \\
    (a) \: Use\, the\, Sensitivity\, Formula\, to\, give\, a\, prediction\, for\, the\, nonzero\, \\
    root \, of\,\; f_{\epsilon }(x) = x^{n} -ax^{n-1} + \epsilon x^{n} \, for\,small\,\epsilon.\\
    \\ (b) \: Find \, the \, nonzero \, root \, and \, compare \, with \, the \, prediction. [/itex]

    2. Relevant equations

    Sensitivity Formula for Roots:
    [itex]\Delta r \approx -\frac{\epsilon g(r)}{f'(r)}[/itex]

    [itex]f'(x) = x^{n-2} (a + xn - an)[/itex]

    3. The attempt at a solution

    Some thoughts, and tries...

    One of the roots for f(x) (without the g(x) and Epsilon) is obviously the constant A.
    [itex]a = \frac{x^{n}}{x^{n-1}}[/itex]

    So if I now plugg terms into the sensitivity root

    [itex]
    \Delta r \approx -\frac{\epsilon a^{n}}{x^{n-2} (a + an - an)}
    \\
    \Delta r \approx - \epsilon \frac{a^{n}}{a^{n-1}}
    [/itex]

    So a prediction of the nonzero root would simply then be

    [itex]r + \Delta r
    \\
    nonzero root \approx a - \epsilon \frac{a^{n}}{a^{n-1}}
    [/itex]

    Would that be correct?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Numerical Analysis, sensitivity root finding.
  1. Numerical analysis (Replies: 1)

  2. Numerical analysis (Replies: 2)

  3. Numerical Analysis (Replies: 3)

Loading...