| course |
course_year |
question_number |
tags |
title |
year |
Numerical Analysis |
IB |
65 |
IB |
2006 |
Numerical Analysis |
|
4.I.8D |
2006 |
(a) Given the data
\begin{tabular}{c|r|r|r|r}
$x_{i}$ & $-1$ & 0 & 1 & 3 \
\hline$f\left(x_{i}\right)$ & $-7$ & $-3$ & $-3$ & 9
\end{tabular}
find the interpolating cubic polynomial $p \in \mathcal{P}_{3}$ in the Newton form, and transform it to the power form.
(b) We add to the data one more value $f\left(x_{i}\right)$ at $x_{i}=2$. Find the power form of the interpolating quartic polynomial $q \in \mathcal{P}_{4}$ to the extended data
\begin{tabular}{c|c|r|r|r|r}
$x_{i}$ & $-1$ & 0 & 1 & 2 & 3 \
\hline$f\left(x_{i}\right)$ & $-7$ & $-3$ & $-3$ & $-7$ & 9
\end{tabular}$.$