On Fréchet differentiability of some non-linear operators occurring in inverse problems : an implicit function theorem approach
Degree GrantorUniversity of Canterbury
Degree NameResearch report
The validity of Newton-Kantorovich methods for the computational solution of inverse problems is directly linked to the Fréchet differentiability of the appropriate non-linear operator. This paper illustrates how use of the implicit function theorem can considerably simplify the analysis of Fréchet differentiability and regularity properties of this underlying operator. Two widely studied boundary and exterior measurement inverse problems are considered and new regularity results are produced.
SubjectsField of Research::01 - Mathematical Sciences
- Engineering: Reports