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Newton's Method & Error Analysis

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data

    (i) Use Newton’s Method and apparent convergence
    to solve x ln(x) = 5 accurate to 3 and 4 significant figures. Start out with x0 = 2. (ii) Directly
    approximate the absolute error on f, i.e. _f = f(x) − f(˜x). (iii) Use the difference between
    the 4 significant figures and 3 significant figures results for x and the error formula to estimate
    _f. You should find that they approximate each other.

    2. Relevant equations

    _f = ef'(x)

    3. The attempt at a solution

    I understand (i), I got 3.77 & 3.769.

    For (ii), I don't understand what f(x) and f(~x) are. I know x is the measured value and ~x is the true value, but what are they in this case?

    For (iii) do we take the difference to be the absolute error and the multiple it by the derivative at the true value?
     
  2. jcsd
  3. Nov 17, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    x is the solution you get using Newton's method and ~x is the "true" value. You can't know ~x, that's why they say "approximate".
     
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