INVERSION OF TRACE FORMULAS FOR A STURM-LIOUVILLE OPERATOR

作     者：Xiang Xu Jian Zhai 

作者机构：School of Mathematical SciencesZhejiang UniversityHangzhouChina Institute for Advanced StudyThe Hong Kong University of Science and TechnologyHong KongChina 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2022年第40卷第3期

页      面：396-414页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：partly supported by NSFC grant No.11621101,12071430 the Fundamental Research Funds for the Central Universities partially supported by Research Grant Council of Hong Kong,China(GRF grailt 16305018). 

主　　题：Inverse spectral problem Sturm-Liouville operator Trace formulas 

摘      要：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.Instead of inverting the map from density to spectral data directly,we propose a novel method to reconstruct the density based on inverting a sequence of trace formulas which bridge the density and its spectral data clearly in terms of a series of nonlinear integral equations.Numerical experiments are presented to verify the validity and effectiveness of the proposed numerical algorithm.The impact of different parameters involved in the algorithm is also discussed.