{"title":"带分数阶导数的倒向热方程的Levenberg-Marquardt正则化","authors":"P. Pornsawad, C. Böckmann, Wannapa Panitsupakamon","doi":"10.1553/etna_vol57s67","DOIUrl":null,"url":null,"abstract":". The backward heat problem with time-fractional derivative in Caputo’s sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg–Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative\",\"authors\":\"P. Pornsawad, C. Böckmann, Wannapa Panitsupakamon\",\"doi\":\"10.1553/etna_vol57s67\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". The backward heat problem with time-fractional derivative in Caputo’s sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg–Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.\",\"PeriodicalId\":282695,\"journal\":{\"name\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1553/etna_vol57s67\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ETNA - Electronic Transactions on Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1553/etna_vol57s67","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
. The backward heat problem with time-fractional derivative in Caputo’s sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg–Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.
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