By presenting a general framework, some regularization methods for solving linear ill-posed problems are considered in a unified manner. Applications to some specific approaches are illustrated.
We are specially interested in the case that problem (1) is ill-posed; that is, the solutions of (1) do not depend continuously on the data. Now the regularization techniques are required. The traditional method is Ti...We are specially interested in the case that problem (1) is ill-posed; that is, the solutions of (1) do not depend continuously on the data. Now the regularization techniques are required. The traditional method is Tikhonov regularization. In recent years, the concept of entropy was introduced into the study of ill-posed problems and developed the maximum entropy method. It is found that the maximum entropy method has its展开更多
Some converse and saturation results on Tikhonov regularization of nonlinear ill-posed problems are proved and the a posteriori parameter choice yielding optimal rates of convergence is discussed.
The maximum entropy method for linear ill-posed problems with modeling error and noisy data is considered and the stability and convergence results are obtained. When the maximum entropy solution satisfies the "s...The maximum entropy method for linear ill-posed problems with modeling error and noisy data is considered and the stability and convergence results are obtained. When the maximum entropy solution satisfies the "source condition", suitable rates of convergence can be derived. Considering the practical applications, an a posteriori choice for the regularization parameter is presented. As a byproduct, a characterization of the maximum entropy regularized solution is given.展开更多
文摘By presenting a general framework, some regularization methods for solving linear ill-posed problems are considered in a unified manner. Applications to some specific approaches are illustrated.
基金Project supported by the National Natural Science Foundation of China.
文摘We are specially interested in the case that problem (1) is ill-posed; that is, the solutions of (1) do not depend continuously on the data. Now the regularization techniques are required. The traditional method is Tikhonov regularization. In recent years, the concept of entropy was introduced into the study of ill-posed problems and developed the maximum entropy method. It is found that the maximum entropy method has its
基金Project supported by the National Natural Science Foundation of China (Grant No. 9801018).
文摘Some converse and saturation results on Tikhonov regularization of nonlinear ill-posed problems are proved and the a posteriori parameter choice yielding optimal rates of convergence is discussed.
文摘The maximum entropy method for linear ill-posed problems with modeling error and noisy data is considered and the stability and convergence results are obtained. When the maximum entropy solution satisfies the "source condition", suitable rates of convergence can be derived. Considering the practical applications, an a posteriori choice for the regularization parameter is presented. As a byproduct, a characterization of the maximum entropy regularized solution is given.
