{"title":"奇异黑箱矩阵的前置条件","authors":"W. Turner","doi":"10.1145/1073884.1073930","DOIUrl":null,"url":null,"abstract":"This paper develops preconditioners for singular black box matrix problems. We introduce networks of arbitrary radix switches for matrices of any square dimension, and we show random full Toeplitz matrices are adequate switches for these networks. We also show a random full Toeplitz matrix to satisfy all requirements of the Kaltofen-Saunders black box matrix rank algorithm without requiring a diagonal multiplier.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Preconditioners for singular black box matrices\",\"authors\":\"W. Turner\",\"doi\":\"10.1145/1073884.1073930\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper develops preconditioners for singular black box matrix problems. We introduce networks of arbitrary radix switches for matrices of any square dimension, and we show random full Toeplitz matrices are adequate switches for these networks. We also show a random full Toeplitz matrix to satisfy all requirements of the Kaltofen-Saunders black box matrix rank algorithm without requiring a diagonal multiplier.\",\"PeriodicalId\":311546,\"journal\":{\"name\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1073884.1073930\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1073884.1073930","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper develops preconditioners for singular black box matrix problems. We introduce networks of arbitrary radix switches for matrices of any square dimension, and we show random full Toeplitz matrices are adequate switches for these networks. We also show a random full Toeplitz matrix to satisfy all requirements of the Kaltofen-Saunders black box matrix rank algorithm without requiring a diagonal multiplier.
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