## 留言板

 引用本文: 康传刚, 贺国强. 求解非线性不适定的混合Newton-Tikhonov迭代法[J]. 应用数学和力学, 2009, 30(6): 690-700.
KANG Chuan-gang, HE Guo-qiang. A Mixed Newton-Tikhonov Method for Nonlinear Ⅲ-Posed Problems[J]. Applied Mathematics and Mechanics, 2009, 30(6): 690-700. doi: 10.3879/j.issn.1000-0887.2009.06.008
 Citation: KANG Chuan-gang, HE Guo-qiang. A Mixed Newton-Tikhonov Method for Nonlinear Ⅲ-Posed Problems[J]. Applied Mathematics and Mechanics, 2009, 30(6): 690-700.

• 中图分类号: O241

## A Mixed Newton-Tikhonov Method for Nonlinear Ⅲ-Posed Problems

• 摘要: 鉴于Newton型方法在实际计算中计算量可能非常大，因此提出了一种一步Newton结合若干步简化Newton的混合Newton-Tikhonov方法，并且在一定条件下证明了该方法的收敛性和稳定性．数值试验表明，在减少计算量方面该方法相对于经典的Newton方法有明显的改善．
•  [1] Hanke M.A regularization Levenberg-Marquardt scheme,with application to inverse groundwater filtration problems[J].Inverse Problems,1997,13(1):79-95. [2] Engl H W,Hanke M,Neubauer A.Regularization of Inverse Problem[M].Dordrecht:Kluwer Academic,1996. [3] Bakushinskii A B,Kokurin M Y.Iterative Methods for Approximate Solution of Inverse Problems[M].Dordrecht: Springer,2004. [4] Kaltenbacher B,Neubauer A,Scherzer O.Iterative Regularization Methods for Nonlinear Ill-Posed Problems[M].Walter de Gruyter,2008. [5] Jin Q N.On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems[J].Math Comp,2000,69(232):1603-1623. [6] Jin Q N.A convergence analysis of the iteratively regularized Gauss-Newton method under the lipschitz condition[J].Inverse Problems,2008,24(4):1-16. [7] Hanke M,Neubauer A,Scherzer O.A convergerce analysis of the Landweber iteration for nonlinear ill-posed problems[J].Numerical Mathematics,1995,72(11):21-37. [8] Deuflhard P,Engl H W,Scherzer O.A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions[J].Inverse Problems,1998,14(5):1081-1106. [9] Deuflhard P.Newton Method for Nonlinear Problems:Affine Invariance and Adaptive Algorithms[M].Berlin Heidelberg:Springer-Verlag,2004. [10] 贺国强，孟泽红.求解热传导反问题的一种正则化Newton型迭代法[J].应用数学和力学，2007，28(4):479-486.

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##### 出版历程
• 收稿日期:  2008-10-14
• 修回日期:  2009-05-14
• 刊出日期:  2009-06-15

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