Abstract The ill-posed problem results in a large variance in parameter estimation. It is difficult to conduct a precision comparison of regularization and truncated singular value decomposition(TSVD) methods when the true values of parameters are unknown. To address this problem, we propose a mean square error relative comparative method. Firstly, we determine the relative deviation of regularization estimation and TSVD estimation relative to least squares estimation, avoiding the dependency of deviation calculation on the true values. Secondly, we utilize the relative deviation and relative standard deviation to determine the relative decreases of root mean square errors, and the optimal solution is determined by comparing the magnitude of relative decreases. Finally, we verify the feasibility and effectiveness of root mean square error relative comparative method through two sets of experiments.
LIN Dongfang,ZHU Kailin,XIE Jian et al. Comparison and Analysis Method of Relative Mean Square Error for Solving Ill-Posed Problems[J]. jgg, 2024, 44(7): 704-708.
LIN Dongfang,ZHU Kailin,XIE Jian et al. Comparison and Analysis Method of Relative Mean Square Error for Solving Ill-Posed Problems[J]. jgg, 2024, 44(7): 704-708.