Abstract
In many inverse problems a functional of u is given by measurements, where u solves a partial differential equation of the type L(p)u+Su=q. Here q is a known source term, and L(p), S are operators, with p as an unknown parameter of the inverse problem. For the numerical reconstruction of p, the heuristically derived Fréchet derivative R' of the mapping $R:p\rightarrow$ "measurementfunctional of u" is often used. We show for three problems---a transport problem in optical tomography, an elliptic equation governing near-infrared tomography, and the wave equation in moving media---that R' is the derivative in the strict sense. Our method is applicable to more general problems than are established methods for similar inverse problems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.