A main problem in adaptive optics is to reconstruct the phase spectrum given noisy phase differences. We present an efficient approach to solve the least-squares minimization problem resulting from this reconstruction, using either a truncated singular value decomposition (TSVD)-type or a Tikhonov-type regularization. Both of these approaches make use of Kronecker products and the generalized s...

In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of th...

In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are an...

An iterative method is introduced for solving noisy, ill-conditioned inverse problems. Analysis of the semi-convergence behavior identifies three error components iteration error, noise error, and initial guess error. A derived expression explains how the three errors are related to each other relative to the number of iterations. The Standard Tikhonov regularization method is just the first it...

We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply ...

Usually when determining parameters with an inverse method, it is assumed that parameters or properties, other than those being sought, are known exactly. When such known parameters are uncertain, the inverse solution can be very sensitive to the degree of uncertainty. The stochastic regularization method can be modi ed to reduce this sensitivity. This paper presents such a modi cation. In addi...

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice...