Gram-schmidt orthogonalization procedure

Question

Question:

Gram-Schmidt orthogonalization procedure

Approximate the function x(t)=e^t over the interval (0, 1) using the second order polynomial.

1. From the set of linearly independent function, [1,t,t²], form an orthonormal set of functions.

The inner product is defined as = ∫¹₀ f(t)g(t)dt.

2. Based on this set of orthonormal functions, fit the best approximation in the least square error sense, that is minimize the norm of the error between the function x(t) and its approximation.