An Adaptive Regularization Method for Ill-conditioned Problem

Abstract

In order to solve ill-conditioned problem more efficiently, a new method called Adaptive Regularization Method based on Normal Operator(ARMNO) is proposed. By analyzing weakness of the existing adaptive regularization method, we gave a new regularization strategy for ARMNO. Property shows that ARMNO has stronger regularity than Tikhonov regularization method. For illustration, a measured GPS example is utilized to show ARMNO has higher accuracy than the several commonly used estimation methods, it can be concluded that ARMNO has better results for the solvers of serious ill-conditioned problems.