Aadya Chinubhai

An Exact Penalty Matrix for Cubic Smoothing Splines on Arbitary Knot Vectors

These notes derive the penalty matrix Ω of a cubic smoothing spline from first principles, for an arbitrary knot vector. Starting from the definition of the B-spline basis, we express differentiation as a matrix, integrate the squared second derivative in closed form, and arrive...

An Exact Penalty Matrix for Cubic Smoothing Splines on Arbitary Knot Vectors

These notes derive the penalty matrix Ω of a cubic smoothing spline from first principles, for an arbitrary knot vector. Starting from the definition of the B-spline basis, we express differentiation as a matrix, integrate the squared second derivative in closed form, and arrive...