Differentiability of the objective in a class of coefficient inverse problems. (1st June 2017)

• Record Type: Journal Article
• Authors: Smołka, Maciej
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 11(2017)
• Page Start: 2375
• Page End: 2387
• Publication Date: 2017-06-01
• Subjects: Coefficient inverse problem -- Objective functional -- Fréchet differentiability; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.04.011
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we study the Fréchet differentiability of the objective functional for a quite general class of coefficient inverse problems. We present sufficient conditions for the existence of arbitrary-order differentials as well as formulae for the calculation of first and second order derivatives. The general case theorems are then applied to two real-world geophysical inverse problems.