{"title":"Numerical algorithms for recovering a fractional Sturm-Liouville operator based on trace formulae","authors":"Xiaowen Li, Xiaoying Jiang, Xiang Xu","doi":"10.1007/s11075-024-01926-5","DOIUrl":null,"url":null,"abstract":"<p>This paper explores numerical methods for recovering a density term in a fractional Sturm-Liouville problem using a set of spectra. By applying Lidskii’s theorem, a sequence of trace formulae are derived to elucidate the connections between the unknown coefficients and the complex eigenvalues of a fractional spectra problem. Two efficient algorithms are proposed based on these trace formulae, and their effectiveness is demonstrated through numerical experiments.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01926-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
This paper explores numerical methods for recovering a density term in a fractional Sturm-Liouville problem using a set of spectra. By applying Lidskii’s theorem, a sequence of trace formulae are derived to elucidate the connections between the unknown coefficients and the complex eigenvalues of a fractional spectra problem. Two efficient algorithms are proposed based on these trace formulae, and their effectiveness is demonstrated through numerical experiments.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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