Convergence of Levenberg-Marquardt method for the inverse problem with an interior measurement

doi:10.1515/jiip-2017-0089

CORC > 上海财经大学 > 上海财经大学

	Convergence of Levenberg-Marquardt method for the inverse problem with an interior measurement
	Jiang, Yu 2; Nakamura, Gen 1
刊名	JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
	2019-04
卷号	27 期号:2 页码:195-215
关键词	Levenberg-Marquardt method convergence tangential cone condition interior measurement magnetic resonance elastography storage modulus loss modulus
ISSN号	0928-0219
DOI	10.1515/jiip-2017-0089
英文摘要	The convergence of Levenberg-Marquardt method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so-called scalar model by a single interior measurement. The scalar model is the most simplest model for data analysis used as the modeling partial differential equation in the diagnosing modality called the magnetic resonance elastography which is used to diagnose for instance lever cancer. The convergence of the method is proved by showing that the measurement map which maps the above unknown moduli to the measured data satisfies the so-called the tangential cone condition. The argument of the proof is quite general and in principle can be applied to any similar inverse problem to reconstruct the unknown coefficients of the model equation given as a partial differential equation of divergence form by one single interior measurement. The performance of the method is numerically tested for the two-layered piecewise homogeneous scalar models in a rectangular domain and a circular domain.
WOS研究方向	Mathematics
语种	英语
出版者	WALTER DE GRUYTER GMBH
WOS记录号	WOS:000462750700005
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/301]
专题	上海财经大学
通讯作者	Nakamura, Gen
作者单位	1.Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan; 2.Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Jiang, Yu,Nakamura, Gen. Convergence of Levenberg-Marquardt method for the inverse problem with an interior measurement[J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS,2019,27(2):195-215.
APA	Jiang, Yu,&Nakamura, Gen.(2019).Convergence of Levenberg-Marquardt method for the inverse problem with an interior measurement.JOURNAL OF INVERSE AND ILL-POSED PROBLEMS,27(2),195-215.
MLA	Jiang, Yu,et al."Convergence of Levenberg-Marquardt method for the inverse problem with an interior measurement".JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 27.2(2019):195-215.