Description
1. Consider the function
f(x) = sin(2πx) + cos(3πx), x ∈ [−1, 1]. (1)
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 semilogy scale. Make sure to include both (i) the error computed using the
QR decomposition and (ii) the error computed using the normal equations. Interpret the error behavior. (HINT: It’s related to the condition
number of the matrix in the least-squares problem.)
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