{"title":"如何去除中位数指甲油","authors":"A. Fink","doi":"10.1137/0909064","DOIUrl":null,"url":null,"abstract":"Tukey's median polish is an algorithm for smoothing data in two-way tables. Each iteration lowers the $L_1 $ norm of the residual. For commensurable data the algorithm converges in a finite number of steps. It does not, in general, converge to the least $L_1 $ norm residual. We provide an algorithm that converges in a finite number of steps for any real data and gives the least $L_1 $ residual.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"How to Polish off Median Polish\",\"authors\":\"A. Fink\",\"doi\":\"10.1137/0909064\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Tukey's median polish is an algorithm for smoothing data in two-way tables. Each iteration lowers the $L_1 $ norm of the residual. For commensurable data the algorithm converges in a finite number of steps. It does not, in general, converge to the least $L_1 $ norm residual. We provide an algorithm that converges in a finite number of steps for any real data and gives the least $L_1 $ residual.\",\"PeriodicalId\":200176,\"journal\":{\"name\":\"Siam Journal on Scientific and Statistical Computing\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siam Journal on Scientific and Statistical Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/0909064\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam Journal on Scientific and Statistical Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/0909064","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Tukey's median polish is an algorithm for smoothing data in two-way tables. Each iteration lowers the $L_1 $ norm of the residual. For commensurable data the algorithm converges in a finite number of steps. It does not, in general, converge to the least $L_1 $ norm residual. We provide an algorithm that converges in a finite number of steps for any real data and gives the least $L_1 $ residual.
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