A new method for finding the optimal smoothing parameter for the abstract smoothing spline

摘要

In this paper, we present a new method for finding the optimal smoothing parameter α for the abstract smoothing spline α. The latter is defined as the solution of the minimization problem σαargmin{αTx{double pipe}~2+{double pipe}Ax-z{double pipe}~2, and, given an estimate for the noise, the standard choice for α is that σα should satisfy the residual equation {double pipe}Aσα-z{double pipe}=ε. Whereas the classical algorithm for solving this equation based on Newton's method converges quadratically, our new method can have any given order of convergence.