求解非线性不适定的混合Newton-Tikhonov迭代法

康传刚; 贺国强

doi:10.3879/j.issn.1000-0887.2009.06.008

求解非线性不适定的混合Newton-Tikhonov迭代法

doi: 10.3879/j.issn.1000-0887.2009.06.008

上海大学数学系,上海 200444

基金项目: 上海市重点学科资助项目(S30104);上海市教委重点学科建设资助项目(J50101)

详细信息

作者简介:
康传刚(1978- ),男,山东人,博士(E-mail:ckang78@sohu.com);贺国强(1946- ),男,上海人,教授(联系人.E-mail:gqhe@staff.shu.edu.cn).

中图分类号: O241
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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

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

Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

摘要

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．
- 非线性不适定问题 /
- 热传导反问题 /
- 混合Newton-Tikhonov方法 /
- 收敛性 /
- 稳定性
Abstract: Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems and attract extensive attention of people.However,the computational cost of Newton type methods may be very large because of the complexity of practical problems.A mixed NewtonTikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method was proposed.The convergence and stability of this method were proved under some conditions.Numerical experiments show that the new method has obvious improvement over the classical Newton method in the reduction of the computational cost.
- nonlinear ill-posed problem /
- inverse heat conduction problem /
- mixed Newton-Tikhonov method /
- convergence /
- stability

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参考文献(10)

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