• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.909-920
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• 2011

A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

• Journal of IKEEE
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• v.4 no.2 s.7
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• pp.249-256
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• 2000

In EIT(electrical impedance tomography), the internal resistivity(or conductivity) distribution of the unknown object is estimated using the boundary voltage data induced by different current patterns using various reconstruction algorithms. In this paper, we present a regularized modified Newton-Raphson(mNR) scheme which employs additional a priori information in the cost functional as soft constraint and the weighting matrices in the cost functional are selected based on the exponentially weighted least square criterion. The computer simulation for the 32 channels synthetic data shows that the reconstruction performance of the proposed scheme is improved compared to that of the conventional regularized mNR at the expense of slightly increased computational burden.

• Journal of Energy Engineering
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• v.10 no.3
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• pp.183-187
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• 2001

Impedance imaging for binary mixture is a kind of nonlinear inverse problem, which is usually solved iteratively by the Newton-Raphson method. Then, the ill-posedness of Hessian matrix often requires the use of a regularization method to stabilize the solution. In this study, the Levenberg-Marquredt regularization method is introduced for the binary-mixture system with various resistivity contrasts (1:2∼1:1000). Several mixture distribution are tested and the results show that the Newton-Raphson iteration combined with the Levenberg-Marquardt regularization can reconstruct reasonably good images.

• Journal of the Korean Solar Energy Society
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• v.25 no.1
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• pp.87-96
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• 2005

본 논문은 압력차로 인한 유체의 유동장에서 서스펜션의 입자 밀도를 분포 규명하기 위해 적용할 수 있는 Electric Impedance Tomography (EIT)의 새로운 기법에 대한 효율성을 다루고 있다. Regularized Newton-Raphson iterative method를 근간으로 inverse problem의 해를 구하는데, 이는 곧 목적 함수(object function)를 몇 가지의 제한조건(constraints) 하에서 최소화시키는 과정이라 할 수 있다. 한편, 관련 forward problem은 유한요소법(FEM)을 이용하여 해결하며, 기존의 연구와는 달리 선형 형상 함수(linear shape function)를 이용하여 전도도가 연속적인 물성치로 유동장에 분포되어 있는 것으로 가정하였다. 여러 경우의 test run에 대한 결과는 본 논문에서 적용한 방법론의 타당성을 보여 주고 있다. 태양에너지의 추출을 위해 직접촉식 열교환기가 종종 이용되고 있는데, 본 연구는 열교환기 내부의 분산 유체에 대한 해석에 일조를 할 수 있을 것으로 기대된다.