Let g1(t).......gn(t) be prescribed, linearly independent functions. Explain how to best approximate a function f(t) by a

Question:

Let g1(t).......gn(t) be prescribed, linearly independent functions. Explain how to best approximate a function f(t) by a linear combination Cngn (t) when the least squares error is measured in a weighted L2 norm ||f||2 = ʆbaf(t)2 w(t) dt with weight function w(t) > 0