# Numerical Analysis/Neville's algorithm quiz

1

What is the correct form of Neville's Algorithm?

 ${\displaystyle P_{i,j}(x)={\frac {(x_{j}-x)P_{i,j-1}(x)+(x-x_{i})P_{i+1,j}(x)}{x_{j}-x_{i}}}}$. ${\displaystyle P_{i,j}(x)={\frac {(x_{j}+x)P_{i,j-1}(x)+(x-x_{i})P_{i+1,j}(x)}{x_{j}+x_{i}}}}$. ${\displaystyle P_{i,j}(x)={\frac {(x_{j}-x)P_{i,j+1}(x)+(x-x_{i})P_{i-1,j}(x)}{x_{j}-x_{i}}}}$.

2

When is Neville's Algorithm most useful?

 When we only want the coefficients of the polynomial. When we only want the interpolated value of the polynomial. When we want both the coefficients and the interpolated value of the polynomial.

3

Approximate ${\displaystyle {\sqrt {x}}}$ at ${\displaystyle f(6)}$ using ${\displaystyle x_{0}=1,x_{1}=4,}$ and ${\displaystyle x_{2}=9}$.

 2.07143 2.14565 2.23423