A Lavrentiev type regularization technique for solving elliptic boundary control problems with pointwise state constraints is considered. The main concept behind this regularization is to look for controls in the range of the adjoint control-to-state mapping. After investigating the analysis of the method, a semismooth Newton method based on the optimality conditions is presented. The theoretic...

This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization s...

We propose a nonlinear image restoration method that uses the generalized radial basis function network (GRBFN) and a regularization method. The GRBFN is used to estimate the nonlinear blurring function. The regularization method is used to recover the original image from the nonlinearly degraded image. We alternately use the two estimation methods to restore the original image from the degrade...

In this paper we consider the regularity of the trust region-cg algorithm, when it is applied to nonlinear ill-posed iverse problems. The trust region algorithm can be viewed as a regularization method, but it diiers from the traditional regularization method, because no penalty term is need. Thus, the determing of the so-called regular-ization parameter in a standard regularization method is a...

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solu...

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 ...

We consider a “local” Tikhonov regularization method for ill-posed Volterra problems. In addition to leading to efficient numerical schemes for inverse problems of this type, a feature of the method is that one may impose varying amounts of local smoothness on the solution, i.e., more regularization may be applied in some regions of the solution’s domain, and less in others. Here we present pro...

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self-forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) mode-sum regularization method. We also address the gauge-regularization problem...

This paper gives a comprehensive numerical analysis of a multiscale method for equilibrium Navier Stokes equations. The method includes pressure regularization and eddy viscosity stabilizations both acting only on the finest scales. This method allows for equal order velocity-pressure spaces as well as the linear constant pair and the usual (Pk, Pk−1) pair. We show the method is optimal in a na...

In this paper, identifying the initial value for high dimension heat equation with inhomogeneous source on a spherical symmetric domain is investigated. The truncation regularization method is a powerful technique for solving this inverse problem. We prove the convergence estimates between the regularization solution and the exact solution under the prior and the posterior regularization parame...