8.18∗ Show, using integration by parts, that the penalty term of Equation

(8.11) can be written as:

 b a

(f(x))2dx = f

Kf.

Show further that the function S

(f) of Equation (8.11) can be written as:

S(f)=(y − f)



(y −

f) + νf

Kf, and deduce that the minimising value of F is F = (I + νK)

−1y.