Application Of Quasi-boundary Value Regularization Method In Two Kinds Of Inverse Problems

In this paper,we mainly consider using the quasi-boundary value regularization method to solve the Cauchy problem of the three-dimensional Laplace equation and the Cauchy problem of the three-dimensional Helmholtz equation.These two kinds of problems are serious ill-posed problems.Under certain conditions,their solutions are discontinuous and depend on the initial data.In this paper,the quasi-boundary value regularization method is used to restore the dependence of the solution on the data.And the paper give the error estimates between the exact solution and the approximate solution under the prior regularization parameter selection rule and the posterior regularization parameter selection rule,respectively.At the same time,the effectiveness and feasibility of this method are verified by numerical examples.