Inversion of trace formulas for a Sturm-Liouville operator
Numerical Analysis
2019-07-01 v1 Numerical Analysis
Abstract
This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new numerical scheme to reconstruct the density. Numerical experiments are presented to verify the validity and effectiveness of the numerical scheme.
Keywords
Cite
@article{arxiv.1906.12108,
title = {Inversion of trace formulas for a Sturm-Liouville operator},
author = {Xiang Xu and Jian Zhai},
journal= {arXiv preprint arXiv:1906.12108},
year = {2019}
}