{"title":"矩阵函数微分的HOL理论","authors":"Yuhan Nie, Zhiping Shi, Aixuan Wu, Ximeng Li, Guohui Wang, Yong Guan","doi":"10.1109/TASE.2019.00-10","DOIUrl":null,"url":null,"abstract":"The differential of matrix functions(DMF) plays an important role in mathematics and engineering. Common applications of it are found in optimization analysis, computer vision, robotics, etc. In this paper, a formal method based on HOL is used to construct the DMF based on Fréchet differential in matrix space. In order to illustrate the practical effectiveness of our work, we use our formalization to verify a property of matrix exponential.","PeriodicalId":183749,"journal":{"name":"2019 International Symposium on Theoretical Aspects of Software Engineering (TASE)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A HOL Theory of the Differential for Matrix Functions\",\"authors\":\"Yuhan Nie, Zhiping Shi, Aixuan Wu, Ximeng Li, Guohui Wang, Yong Guan\",\"doi\":\"10.1109/TASE.2019.00-10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The differential of matrix functions(DMF) plays an important role in mathematics and engineering. Common applications of it are found in optimization analysis, computer vision, robotics, etc. In this paper, a formal method based on HOL is used to construct the DMF based on Fréchet differential in matrix space. In order to illustrate the practical effectiveness of our work, we use our formalization to verify a property of matrix exponential.\",\"PeriodicalId\":183749,\"journal\":{\"name\":\"2019 International Symposium on Theoretical Aspects of Software Engineering (TASE)\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 International Symposium on Theoretical Aspects of Software Engineering (TASE)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TASE.2019.00-10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 International Symposium on Theoretical Aspects of Software Engineering (TASE)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TASE.2019.00-10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A HOL Theory of the Differential for Matrix Functions
The differential of matrix functions(DMF) plays an important role in mathematics and engineering. Common applications of it are found in optimization analysis, computer vision, robotics, etc. In this paper, a formal method based on HOL is used to construct the DMF based on Fréchet differential in matrix space. In order to illustrate the practical effectiveness of our work, we use our formalization to verify a property of matrix exponential.
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