Thread: 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

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 on the set with respect to an appropriate inner product and norm and then expand in terms of these.

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