The Application Of Quasi-Reversibility Regularization Method In Two Kinds Of Inverse Problems

The Cauchy problem of Laplace equation and the analytic continuation problem are two kinds of severely ill-posed problems in inverse problems.This paper considers that the quasi-reversibility regularization method.Compared with the other regularization methods,the advantage of this method is that in the case of no expression of the solution,the regular solution of the problem can be obtained directly by calculation.In this paper,the quasi-reversibility regularization method is used to solve the Cauchy problem of Laplace equation and the analytic continuation problem,and the corresponding error estimates are obtained with appropriate regularization parameters,finally,several numerical examples are given to illustrate the feasibility and effectiveness of the quasi-reversibility regularization method.