1. ## Numerical analysis

For the following function, let x0=0, x1=0.6, and x2=0.9. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.45), and find the actual error.
f(x)=cosx

2. Originally Posted by wvlilgurl
For the following function, let x0=0, x1=0.6, and x2=0.9. Construct interpolation polynomials of degree at most one and at most two to approximate f(0.45), and find the actual error.
f(x)=cosx
There are many ways of doing this, what methods have you been shown?

My personal favourite is to construct an orthonormal basis of polynomials up to degree $2$ on the set $\{0,1,2\}$ with respect to an appropriate inner product and norm and then expand $\cos(x)$ in terms of these.

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3. Thats the problem. Our professor has not shown us how to do these and the book only gives us formulas they have proven.