1. Consider the function
f(x) = sin(2πx) + cos(3πx), x ∈ [−1, 1].
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Evaluate the function values at n evenly spaced points. You get to choose n. For d from 0 to n − 1, compute the least-squares coefficients of a polynomial of degree d with the same training data using both the QR method and the normal equations.
2. For each trained polynomial compute testing error on a set of testing data, which you will generate. Plot the error ed versus d on a semil-ogy scale. Make sure to include both (i) the error computed using the QR decomposition and (ii) the error computed using the normal equa-tions. Interpret the error behavior. (HINT: It’s related to the condition number of the matrix in the least-squares problem.)
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