Two Regularization Methods For Analytic Continuation

The problems of numerical analytic continuation are frequently encountered in many practical applications. These problems are well known to be severely ill-posed and therefore several regularization methods have been suggested for solving them. In this paper, we consider the problem of analytic continuation of the analytic function f(z)=f(x+iy) on a strip domainΩ={z=x+iy∈C|x∈R,|y|<≤y0}, where the data are given only on the real axis.We propose two methods—a modified kernel method and an approximation method by harmonic functions to solve this problem and obtain the convergence estimates between the exact solutions and its approximations. Finally, some numerical examples are provided. The analysis of the theory and the numerical results show that the modified kernel method and approximation method by harmonic functions are effective.