Optimal Numerical Methods for Choosing an Optimal Regularization Parameter

Abstract

Five different computational methodologies are studied and evaluated for the purpose of determining optimal regularization parameters. These methods include the maximum likelihood (ML), the ordinary cross-validation (OCV), the generalized cross-validation (GCV), the L-curve method, and the discrepancy principle (DP). This is the first time that these five methods are compared simultaneously by using the same example problems for the inverse heat transfer problem. Testing results show that the discrepancy principle gives the best estimate of the regularization parameter. In many cases, the OCV and GCV are the second and third best methods, and the L-curve method is the fourth most accurate method among the five methods. The ML method is very stable but always estimates smaller regularization parameters than in the analytical solution.

The authors gratefully acknowledge the financial support of NASA (Grant NAG8-1697).