1.5 Multi-Dimensional Splines скачать в хорошем качестве

1.5 Multi-Dimensional Splines

In this video, we extend smoothing splines to the multidimensional setting and treat the general case in Rn. We move from the one-dimensional construction to the thin-plate spline framework and derive the full solution structure. Topics covered: • Multidimensional smoothing spline formulation • General variational problem in Rn • Thin-plate spline as a special case • Curvature penalty • Euler–Lagrange equation in multiple dimensions • Derivation of the kernel function as the solution • Finite-dimensional representer structure • Conversion of the solution into a linear system