1.5 Multi-Dimensional Splines
Автор: Jingyuan Hu
Загружено: 2026-02-25
Просмотров: 102
Описание:
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
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