A Newton-type method for a transmission problem in inverse scattering

Thorsten Hohage

A Newton-type method for a transmission problem in inverse scattering

Thorsten Hohage

Industrial Mathematics Institute

Research output: Contribution to journal › Article › peer-review

Abstract

The iteratively regularized Gauß-Newton method is applied to solve an inverse transmission problem for the Helmholtz equation, which is known to be nonlinear and severely ill-posed. We first present a simplified proof of the characterization of the Frechet derivative. Based on this result, we describe an efficient numerical implementation including an error analysis. Finally, we investigate the speed of convergence of the Newton iteration both for exact and for noisy data.

Original language	English
Journal	Inverse Problems
Publication status	Published - 1998

Fields of science

101 Mathematics
101020 Technical mathematics

Cite this

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title = "A Newton-type method for a transmission problem in inverse scattering",

abstract = "The iteratively regularized Gau{\ss}-Newton method is applied to solve an inverse transmission problem for the Helmholtz equation, which is known to be nonlinear and severely ill-posed. We first present a simplified proof of the characterization of the Frechet derivative. Based on this result, we describe an efficient numerical implementation including an error analysis. Finally, we investigate the speed of convergence of the Newton iteration both for exact and for noisy data.",

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journal = "Inverse Problems",

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AB - The iteratively regularized Gauß-Newton method is applied to solve an inverse transmission problem for the Helmholtz equation, which is known to be nonlinear and severely ill-posed. We first present a simplified proof of the characterization of the Frechet derivative. Based on this result, we describe an efficient numerical implementation including an error analysis. Finally, we investigate the speed of convergence of the Newton iteration both for exact and for noisy data.

M3 - Article

JO - Inverse Problems

JF - Inverse Problems

ER -