Solutions Of A Class Of Operator Equations Regularization Methods And Applications

As an important class of mathematical physical problems, inverse problem has been developed into a popular research direction.Sloving an inverse problem is to determine the causes based on observation of the effects, and most of them are ill-posed.Two main factors contribute to this.In the first place,the observation data possibly does not belong to the corresponding set of the exact solution, so the approximate solution does not exist in the classic sense; In the second place,the approximate solution is not stable,that is ,the minor changes of observation error of original data may cause the serious error between the approximate solution and the true solution.Thus,it is very difficult to solve the problem numerically. But Regularization technique is an effective method of solving ill-posed inverse problems,its basic idea is that: Using the solution of a series well-posed problem which is appropriate to the original problem to approach the solution of the original problem.The paper presents a new method of iterated regularization for solving operation equation of the first kind, by applying the generalized Arcangeli's criterion to choose the regularization parameter, we obtain the convergence of the regularized solution, and as compared with Tikhonov regularization,the asymptotic order of regularized solution is improved.the paper applies them to the practical problems,such as, numerical differentiation.