An Efficient Linear Solver for Nonlinear Parameter Identification Problems

In this paper, we study some efficient numerical methods for parameter identifications in elliptic systems. The proposed numerical methods are conducted iteratively and each iteration involves only solving positive definite linear algebraic systems, although the original inverse problems are ill-posed and highly nonlinear. The positive definite systems can be naturally preconditioned with their corresponding block diagonal matrices. Numerical experiments are presented to illustrate the efficiency of the proposed algorithms.