... is tested by multiple numerical examples, and we observe that this approach is capable of preserving the shape and the shear moduli of the inclusions well. In particular, this inverse approach performs well even without any regularization when the noise level is not very high. Overall, the proposed approach...

... , Numerical Methods for the Solution of Ill-Posed Problems , Kluwer Academic , Norwell, MA . [18] Li , X. Y. , and Law , S. S. , 2010 , “ Adaptive Tikhonov Regularization for Damage Detection Based on Nonlinear Model Updating ,” Mech. Syst. Signal Process. , 24 , pp. 1646 – 1664 . 10.1016...

... integral equations of the second kind and L-curve based Tikhonov’s regularization method are used to construct the computational scheme of parameter estimation. A numerical case study is presented to demonstrate the efficiency of the regularization method, which takes into account different step lengths...

... a straightforward least-squares method, would be unbound. A regularization technique ( 17 ) can be used to solve the ill-posed problem in the form of minimizing the function 38 χ ( P , λ ) = ‖ B P − U ‖ 2 + λ ‖ P ‖ 2 where matrices U , B , and P represent the left...