On Fréchet differentiability of some non-linear operators occurring in inverse problems : an implicit function theorem approach

Type of content
Discussion / Working Papers
Publisher's DOI/URI
Thesis discipline
Degree name
Research Report
Publisher
University of Canterbury. Dept. of Mathematics
Journal Title
Journal ISSN
Volume Title
Language
Date
1990
Authors
Connolly, Thomas John
Wall, David J. N.
Abstract

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.

Description
Citation
Keywords
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Field of Research::01 - Mathematical Sciences
Rights
Copyright Thomas John Connolly