Logarithmic convergence rates for the identification of a nonlinear Robin coefficient

Kügler, Philipp; Sincich, Eva

doi:10.1016/j.jmaa.2009.06.004

Cited by 6 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Reference [30] applied the Tikhonov regularization method to reconstruct the dynamic force. Reference [31] demonstrated that the Tikhonov regularization method can solve the inverse problem in a stable manner despite the presence of noisy data. Reference [32] identified the shock load on an electroelastic bimorph disk using the Tikhonov regularization method.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Ren

Wang

Liu

et al. 2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal-seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill-conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill-posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

show abstract

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Ren

Wang

Liu

et al. 2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Subsequent research addressed this concern by employing nonsmooth regularizers. Notable contributions in this direction include the works of Burger and Osher [8], Kaltenbacher and Hofmann [30], Kügler and Sincich [34], Resmerita [39], and Resmerita and Scherzer [40], along with other references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances

2023

J. Nonlinear Var. Anal.

View full text Add to dashboard Cite

Deriving convergence rates constitutes a crucial and profound field of investigation, carrying significant implications in both theoretical and practical contexts. This study focuses on establishing new convergence rates for nonlinear inverse problems concerning the identification of variable parameters in an abstract variational problem. We employ the energy least squares and output least squares methods to study the inverse problem in an optimization framework. The convergence rates are given in terms of the renowned Bregman distance associated with a convex regularizer. An intriguing aspect of the derived convergence rates is that they do not necessitate any smallness condition, making them applicable to a wide array of practical models.

show abstract

“…In this paper we are interested in the numerical reconstruction issue of the unknown and damaged boundary Γ I from the data collected on the accessible part of the boundary Γ A , that is the Cauchy data pair (u| Γ A , Φ). Boundary and parameter identification results related to this stationary inverse problem has been provided by many authors [1,2,3,5,9,4,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Discretized Tikhonov regularization for Robin boundaries localization

Cao

Pereverzev

Sincich

2014

Applied Mathematics and Computation

View full text Add to dashboard Cite

We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair collected on the accessible part of the boundary. We combine a linearization argument with a Tikhonov regularization approach for the local reconstruction of the unknown defect. Moreover, we discuss the regularization parameter choice by means of the so called balancing principle and we present some numerical tests that show the efficiency of our method.

show abstract

Logarithmic convergence rates for the identification of a nonlinear Robin coefficient

Cited by 6 publications

References 27 publications

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances

Discretized Tikhonov regularization for Robin boundaries localization

Contact Info

Product

Resources

About