This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods...This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.展开更多
In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear ...In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.展开更多
In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactor...In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.展开更多
In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results...In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.展开更多
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ...An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.展开更多
This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. ...This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.展开更多
基金This work was supported by the National Natural Science Foundation of China
文摘This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.
基金supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)the Shanghai Leading Academic Discipline Project (No. J50101)
文摘In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.
文摘In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.
文摘In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.
文摘An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
文摘This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.
