0
$\begingroup$

Let $(x)=x^4$ be approximated by a polynomial of degree less or equal to 2, which interpolates $x^4$ at x = -1,0,1then the maximum absolute interpolation error over the interval[-1,1] is equal to?

$\endgroup$
1
$\begingroup$

You have three points on $f(x)=x^4$. Find a quadratic $g(x)$ that passes throught these three points. Then you are looking for $\max |f(x)-g(x)|$. Compute it as a function of $x$, take the derivative, set to zero ...

$\endgroup$
  • $\begingroup$ Thank you for the answer. Please explain why we are looking for max | $f(x)$ - g(x) | $\endgroup$ – user479498 Jan 17 '18 at 20:01
  • $\begingroup$ Thank you for the answer. Please explain why we are looking for $\max |f(x)-g(x)|$ . $\endgroup$ – user479498 Jan 17 '18 at 20:03
  • $\begingroup$ Because that is the maximum error between $x^4$ and your quadratic. $\endgroup$ – Ross Millikan Jan 17 '18 at 20:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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