101. Reconstructing Stieltjes Functions from Their Approximate Values: A Search for a Needle in a Haystack
- Author
-
Yury Grabovsky
- Subjects
Optimization and Control (math.OC) ,Applied Mathematics ,FOS: Mathematics ,FOS: Physical sciences ,Numerical Analysis (math.NA) ,Mathematical Physics (math-ph) ,Mathematics - Numerical Analysis ,Mathematics - Optimization and Control ,Mathematical Physics ,78A57, 78A48, 49K40, 30H15 - Abstract
Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic functions mapping complex upper half-plane into itself. Reconstructing such functions from their experimentally measured values at specific frequencies is one of the central problems that we address in this paper. A definitive reconstruction algorithm that produces a certificate of optimality as well as a graphical representation of the uncertainty of reconstruction is proposed. Its effectiveness is demonstrated in the context of the electrochemical impedance spectroscopy., 37 pages, 6 figures
- Published
- 2022