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In this paper, we shall derive and propose an efficient algorithm for simultaneously reconstructing the Robin coefficient and heat flux in an elliptic system from part of the boundary measurements. The uniqueness of the simultaneous identification is demonstrated. The ill-posed inverse problem is formulated into an output least-squares nonlinear and non-convex minimization with Tikhonov regularization, while the regularizing effects of the regularized system are justified. The Levenberg–Marquardt method is applied to change the non-convex minimization into convex minimization, which will be solved by surrogate functional method so as to get the explicit expression of the minimizer. Numerical experiments are provided to show the accuracy and efficiency of the algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the convergence rates of the widely used output least squares method with Tikhonov regularization for the identification of the magnetic permeability in a Maxwell system. By introducing some new techniques, we derive a simple and easily interpretable source condition and guarantee the usual convergence rate O() for the regularized solutions, whereis assumed to be the noise level of the data. More importantly, we finally construct the source functions successfully in two-dimensional spaces. [ABSTRACT FROM PUBLISHER]

In this paper, we are concerned with two efficient algorithms for surface construction. Based on the Gauss equations, a discretized nonlinear equation of the formshould be solved in the process of surface construction. We first consider a regularized fixed-point iterative algorithm for solving the discretized equation, in which we determine the actual regularization parameter by the Morozov discrepancy principle. A two-parameter algorithm is employed for solving the Morozov equation, and the convergence of the regularized fixed-point iterative algorithm is demonstrated. Secondly, we also propose the regularizing Levenberg–Marquardt scheme to solve the discretized equation, in which the regularization parameter is chosen to be a small constant. Numerical experiments are provided to demonstrate the robustness and efficiency of the two algorithms. [ABSTRACT FROM AUTHOR]