Physical Sciences and Mathematics Commons^™

A Newton Root-Finding Algorithm For Estimating The Regularization Parameter For Solving Ill-Conditioned Least Squares Problems, Jodi Mead, Rosemary Renaut

Jodi Mead

We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random variable that follows a X2 distribution. The regularization parameter can then be found so that the optimal cost functional has this property. Under this premise a scalar Newton root-finding algorithm for obtaining the regularization parameter is presented. The algorithm, which uses the singular value decomposition of …