Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm studiyng for my exam of scientific computing, specifically to the subject of interpolation techniques, I'm stuck with this problem:

How many equally spaced nodes must be taken to interpolate the function $f(x) = \exp(x)$ on the interval $[-1,1]$, so that the interpolation error is $0.5 * 10^{-4}$?

I have no idea how to start or what should I do in the exercise. Any help?

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

You have to define the interpolation technique used. If you use linear interpolation between the nodes (which I suspect is what you are doing) you are using the first order Taylor's series. The error term is $\frac {f''(x)(x-a)^2}{2!}$. $x-a$ is at most half your node spacing, which you can choose to get the error low enough. What is the maximum value of $f''(x)$ on $[-1,1]$?

share|improve this answer
    
i think is 2.7182, right? –  franvergara66 Sep 12 '12 at 5:31
    
@Melkhiah66: that's right, so plug that in and you can find $x-a$ from $\frac {e(x-a)^2}{2!} \lt 0.5\cdot 10^{-4}$ –  Ross Millikan Sep 12 '12 at 13:02
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.