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

KANG Chuan-gang; HE Guo-qiang

doi:10.3879/j.issn.1000-0887.2009.06.008

Volume 30 Issue 6

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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. 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. doi: 10.3879/j.issn.1000-0887.2009.06.008

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

doi: 10.3879/j.issn.1000-0887.2009.06.008

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

Received Date: 2008-10-14
Rev Recd Date: 2009-05-14
Publish Date: 2009-06-15

Abstract

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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References(10)

References

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