On the determination of proper regularization parameter : α-weighted BLE via A-optimal design and its comparison with the results derived by numerical methods and ridge regression

Abstract

In this thesis, several numerical regularization methods and the ridge regression, which can help improve improper conditions and solve ill-posed problems, are reviewed. The determination of the optimal regularization parameter via A-optimal design, the optimal uniform Tikhonov-Phillips regularization (α-weighted biased linear estimation), which minimizes the trace of the mean square error matrix MSE(x ̂), is also introduced. Moreover, the comparison of the results derived by A-optimal design and results derived by numerical heuristic methods, such as L-curve, Generalized Cross Validation and the method of dichotomy is demonstrated. According to the comparison, the A-optimal design regularization parameter has been shown to have minimum trace of MSE(x ̂) and its determination has better efficiency.