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31 : Consider a set of four data points: f(0)=3, f(2)=2, f(1)=2 and f(1)=1. Find the best fit polynomial of degree two, p2(x), for the
31: Consider a set of four data points: f(0)=3, f(2)=2, f(1)=2 and f(1)=1. Find the best fit polynomial of degree two, p2(x), for the above data points using least-squares method by answering the following:
- (2 Marks) Write down the matrices, A and b, from the above data.
- (3 Marks) Compute the normal matrix ATA and ATb.
- (5 Marks) Use the results in the previous part to compute the column matrix x=(a0 a1 a2)T, where a0, a1 and a2 are the coefficients of the polynomial p2, and then write the expression of the polynomial p2.
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