CAJ | 학술논문

针对基本解法在求解反问题时的病态特性，将截断奇异值分解（TSVD）、Tikhonov正则化方法应用于所得病态系统方程的求解，采用L曲线法和GCV方法确定其正则参数，并比较了4种组合方法求解的精确性和稳定性。数值算例表明，TSVD方法、Tikhonov正则化方法结合L曲线法和GCV法可有效地处理反问题中的病态特性。
침대기본해법재구해반문제시적병태특성，장절단기이치분해（TSVD）、Tikhonov정칙화방법응용우소득병태계통방정적구해，채용L곡선법화GCV방법학정기정칙삼수，병비교료4충조합방법구해적정학성화은정성。수치산례표명，TSVD방법、Tikhonov정칙화방법결합L곡선법화GCV법가유효지처리반문제중적병태특성。
In order to resolve ill-conditioned problems existing in the regularization M FS for the 2D boundary conditions identification potential problems ,suitable regularization methods are nee‐ded .The truncated singular value decomposition (TSVD )method and Tikhonov regularization method are used to solve linear systems with a large number of conditions respectively .The L-curve and generalized cross validation (GCV ) methods are employed to determine the optimal reg‐ularization parameters .Furthermore ,the accuracy and robustness of regularization solution for four combined methods are investigated .Numerical results show that TSVD method and Tik‐honov method can effectively solve the ill posed system caused by inverse problems .Through ap‐plying to L-curve method and GCV method ,continuous regularization parameter for Tikhonov method can be confirmed reasonably .