Back to Search
Start Over
Reconstructing Stieltjes Functions from Their Approximate Values: A Search for a Needle in a Haystack
- Source :
- SIAM Journal on Applied Mathematics. 82:1135-1166
- Publication Year :
- 2022
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2022.
-
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.<br />37 pages, 6 figures
Details
- ISSN :
- 1095712X and 00361399
- Volume :
- 82
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Applied Mathematics
- Accession number :
- edsair.doi.dedup.....e90039cdbe7fecfb55afa717d2680122