{"title":"关于对角结构矩阵的计算","authors":"S. Hossain, M. S. Mahmud","doi":"10.1109/HPEC.2019.8916325","DOIUrl":null,"url":null,"abstract":"We present a storage scheme for storing matrices by diagonals and algorithms for performing matrix-matrix and matrix-vector multiplication by diagonals. Matrix elements are accessed with stride-1 and involve no indirect referencing. Access to the transposed matrix requires no additional effort. The proposed storage scheme handles dense matrices and matrices with special structure e.g., banded, triangular, symmetric in a uniform manner. Test results from preliminary numerical experiments with an OpenMP implementation of our method are encouraging.","PeriodicalId":184253,"journal":{"name":"2019 IEEE High Performance Extreme Computing Conference (HPEC)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On Computing with Diagonally Structured Matrices\",\"authors\":\"S. Hossain, M. S. Mahmud\",\"doi\":\"10.1109/HPEC.2019.8916325\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a storage scheme for storing matrices by diagonals and algorithms for performing matrix-matrix and matrix-vector multiplication by diagonals. Matrix elements are accessed with stride-1 and involve no indirect referencing. Access to the transposed matrix requires no additional effort. The proposed storage scheme handles dense matrices and matrices with special structure e.g., banded, triangular, symmetric in a uniform manner. Test results from preliminary numerical experiments with an OpenMP implementation of our method are encouraging.\",\"PeriodicalId\":184253,\"journal\":{\"name\":\"2019 IEEE High Performance Extreme Computing Conference (HPEC)\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 IEEE High Performance Extreme Computing Conference (HPEC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/HPEC.2019.8916325\",\"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 IEEE High Performance Extreme Computing Conference (HPEC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/HPEC.2019.8916325","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present a storage scheme for storing matrices by diagonals and algorithms for performing matrix-matrix and matrix-vector multiplication by diagonals. Matrix elements are accessed with stride-1 and involve no indirect referencing. Access to the transposed matrix requires no additional effort. The proposed storage scheme handles dense matrices and matrices with special structure e.g., banded, triangular, symmetric in a uniform manner. Test results from preliminary numerical experiments with an OpenMP implementation of our method are encouraging.
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