In this paper, we prove a sharp stability estimate for the problem of analytic continuation. Based on the obtained stability estimate, a generalized Tikhonov regularization is provided and theâ€¦ (More)

In this paper, we study a non-characteristic Cauchy problem for a radially symmetric inverse heat conduction equation in a two-layer domain. This is a severely ill-posed problem in the sense that theâ€¦ (More)

It is well-known that Gaussian filter is the most important model in image denoising. However, the inverse of the Gaussian model for image sharpening is seriously ill-posed. In this paper, we proposeâ€¦ (More)

Numerical fractional differentiation is a classical ill-posed problem in the sense that a small perturbation in the data can cause a large change in the fractional derivative. In this paper, weâ€¦ (More)

Based on a mathematical model of laser beams, we present a spectral Galerkin method for solving a Cauchy problem of the Helmholtz equation in a rectangle, where the Cauchy data pairs are given at yâ€‰=â€¦ (More)