Keung, Yee Lo; Zou, Jun An efficient linear solver for nonlinear parameter identification problems. (English) Zbl 0978.35096 SIAM J. Sci. Comput. 22, No. 5, 1511-1526 (2001). Summary: 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. Cited in 15 Documents MSC: 35R30 Inverse problems for PDEs 65N21 Numerical methods for inverse problems for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:parameter identifications in elliptic systems; positive definite linear algebraic systems; block diagonal matrices; numerical experiments PDFBibTeX XMLCite \textit{Y. L. Keung} and \textit{J. Zou}, SIAM J. Sci. Comput. 22, No. 5, 1511--1526 (2000; Zbl 0978.35096) Full Text: DOI