By checking the "yes" answer below I confirm
1. that I have neither given nor received unauthorized aid to answer the questions of this assignment.
2. I agree to follow the rules in regard of online assignments as post
...
By checking the "yes" answer below I confirm
1. that I have neither given nor received unauthorized aid to answer the questions of this assignment.
2. I agree to follow the rules in regard of online assignments as posted in the course outline
3. I used only octave or Matlab to solve the questions (I am allowed to consult all course material and my own notes)
Select one:
a. Yes I agree
b. No I do not agree
Your answer is correct.
The correct answer is: Yes I agree
You have to solve an equation f(x) = 0 with a precision below a relative error of 10−5 . If ∣ f(xr) ∣ < 10−5 then
∣ xr ∣
Select one:
a. you have found an approximation xr to the specified precision
b. you have found an approximation xr to the specified precision as long as xr ≠ 0
c. you have found an approximation xr to the specified precision if xr is not a multiple root
d. you can't conclude anything
Your answer is incorrect.
The quantity |f(xr)|, which is the backward error, doesn't tell you anything about |r − xr| which is the absolute error.
Similarly ∣ f(xr) ∣ doesn't tell you anything about ∣ r−xr ∣ which is the relative error you want to have below the specified
∣ xr ∣ xr
tolerance.
Reference: lecture on backward and forward errors in Lesson 2 "Solving nonlinear equations". The correct answer is: you can't conclude anything
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Find the absolute backward and forward error for the following functions, where the true root is r = 0.5 and the
approximated root is xr = 0.48.
Fill out the following table to answer the question (use as many digits as possible)
The absolute forward error is for all cases |r − xr| = 0.02.
The absolute backward error is different for each case and is computed as |f(xr)|.
The important element to understand here: even with a same forward error, one can have different backward errors. This problem illustrates once more that computing the backward error doesn't tell us anything about the forward error. Reference: lecture on forward and backward errors in Lesson 2 "Solving nonlinear equations"
We want to apply the fixed point method to solve the equation x = g(x).
Choose among the following examples of functions g(x) which will lead to a converging fixed point algorithm when using the intia
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