Using B-splines, the rows of XB have only p − 1 nonzero entries. Show that the inner product matrix XT BXB is banded and find its bandwidth. Can this structure be exploited in the computation of...

Using B-splines, the rows of XB have only p − 1 nonzero entries. Show that the inner product matrix XT BXB is banded and find its bandwidth. Can this structure be exploited in the computation of

            A(λ)y = X(XT X + λ2pD) −1 XT

when the number of knots n is large?