Quadratic interpolation means the following: If we are given a table of values $y_i=f(x_i), 0\leq i\leq 2n$, then on each interval $[x_{2j},x_{2j+2}], 0\leq j\leq n-1$,the quadratic interpolating polynomial is used on that interval to interpolate the data.
a)How accurately can we determine $\sin x$ by quadratic interpolation, given a table of $\sin x$ to $10$ decimal places,for $x$ in $[0,2]$ for $2n=200$ values?
b)If we want to calculate the value of $\cos x$ by quadratic interpolation accurate to five decimal places for any $x$ in $[0,\pi ]$, what is the minimum number of data points we must have? ( i.e. find the value of 2n so that the error is less than $\frac{1}{2}\times 10^{-5}$)
My question:I need any hint to solve this prolem.I do not know how to solve it infact I do not understand the quadratic interpolation definition given above.Please help me.Thanks.
