Optimally Generalized Regularization Methods for Solving Linear Inverse Problems 反算問題演講－3/27(二)10:00-11:002012/03/15
講者: 劉進賢 特聘教授 (任教於國立台灣大學土木工程學系)
演講題目: Optimally Generalized Regularization Methods for Solving Linear Inverse Problems
演講時間: 2012/03/27 (二)上午10:00-11:00
For solving ill-posed linear inverse problems, we modify the Tikhonov regularization method by proposing three different preconditioners, and the resultant linear systems are equivalent to the original one without dropping out the regularized term on the right-hand side. As a consequence, the new regularization methods can cover both the regularization effect and the accuracy of solution. The coefficient matrix is arranged to be equilibrated or diagonally dominated by deriving the optimal scales in the introduced preconditioning matrix. Then we apply the iterative scheme derived from the regularized linear system to find the solution of ill-posed linear inverse problem. The presently proposed optimally generalized regularization methods are able to overcome the ill-posedness of the linear inverse problems.