{"title":"二维函数数值微分的TSVD方法","authors":"Zhen-yu Zhao, C. Yue","doi":"10.1109/CSO.2010.11","DOIUrl":null,"url":null,"abstract":"Numerical is a a classical ill-posed problem. In this paper, we propose a new method for numerical differentiation of bivariate functions. The truncated singular value decomposition (TSVD)regularization approach of weighted generalized solution for reasonable equations has been introduced to deal with the ill-posed ness of the problem. We show that the method can be realized by the discrete sine transform. Theoretical and numerical results show that the method is effective.","PeriodicalId":427481,"journal":{"name":"2010 Third International Joint Conference on Computational Science and Optimization","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The TSVD Method for Numerical Differentiation of 2D Functions\",\"authors\":\"Zhen-yu Zhao, C. Yue\",\"doi\":\"10.1109/CSO.2010.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Numerical is a a classical ill-posed problem. In this paper, we propose a new method for numerical differentiation of bivariate functions. The truncated singular value decomposition (TSVD)regularization approach of weighted generalized solution for reasonable equations has been introduced to deal with the ill-posed ness of the problem. We show that the method can be realized by the discrete sine transform. Theoretical and numerical results show that the method is effective.\",\"PeriodicalId\":427481,\"journal\":{\"name\":\"2010 Third International Joint Conference on Computational Science and Optimization\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Third International Joint Conference on Computational Science and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CSO.2010.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Third International Joint Conference on Computational Science and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CSO.2010.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The TSVD Method for Numerical Differentiation of 2D Functions
Numerical is a a classical ill-posed problem. In this paper, we propose a new method for numerical differentiation of bivariate functions. The truncated singular value decomposition (TSVD)regularization approach of weighted generalized solution for reasonable equations has been introduced to deal with the ill-posed ness of the problem. We show that the method can be realized by the discrete sine transform. Theoretical and numerical results show that the method is effective.
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