{"title":"用CORDIC进行有效的复矩阵变换","authors":"N. D. Hemkumar, Joseph R. Cavallaro","doi":"10.1109/ARITH.1993.378101","DOIUrl":null,"url":null,"abstract":"A two-sided unitary transformation (Q transformation) structured to permit integrated evaluation and application using CORDIC primitives is introduced. The Q transformation is shown to be useful as an atomic operation in parallel arrays for computing the eigenvalue/singular value decomposition of Hermitian/arbitrary matrices, and three specific Q transformations that are needed in such arrays are identified. Issues related to the use of CORDIC for complex arithmetic are addressed, and implementations in both conventional (nonredundant) CORDIC and redundant and online modifications to CORDIC are described. If the time to compute a CORDIC operation in nonredundant CORDIC is T/sub c/, the Q transformations identified here can be evaluated and/or applied in 2T/sub c/ using four CORDIC modules for maximum concurrency. In either case, 0.5 T/sub c/ is required to account for scale factor correction. It is shown that a Q transformation can be evaluated and/or applied in /spl ap/10n, where n is the desired bit-precision.<<ETX>>","PeriodicalId":414758,"journal":{"name":"Proceedings of IEEE 11th Symposium on Computer Arithmetic","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Efficient complex matrix transformations with CORDIC\",\"authors\":\"N. D. Hemkumar, Joseph R. Cavallaro\",\"doi\":\"10.1109/ARITH.1993.378101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A two-sided unitary transformation (Q transformation) structured to permit integrated evaluation and application using CORDIC primitives is introduced. The Q transformation is shown to be useful as an atomic operation in parallel arrays for computing the eigenvalue/singular value decomposition of Hermitian/arbitrary matrices, and three specific Q transformations that are needed in such arrays are identified. Issues related to the use of CORDIC for complex arithmetic are addressed, and implementations in both conventional (nonredundant) CORDIC and redundant and online modifications to CORDIC are described. If the time to compute a CORDIC operation in nonredundant CORDIC is T/sub c/, the Q transformations identified here can be evaluated and/or applied in 2T/sub c/ using four CORDIC modules for maximum concurrency. In either case, 0.5 T/sub c/ is required to account for scale factor correction. It is shown that a Q transformation can be evaluated and/or applied in /spl ap/10n, where n is the desired bit-precision.<<ETX>>\",\"PeriodicalId\":414758,\"journal\":{\"name\":\"Proceedings of IEEE 11th Symposium on Computer Arithmetic\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of IEEE 11th Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1993.378101\",\"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 IEEE 11th Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1993.378101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Efficient complex matrix transformations with CORDIC
A two-sided unitary transformation (Q transformation) structured to permit integrated evaluation and application using CORDIC primitives is introduced. The Q transformation is shown to be useful as an atomic operation in parallel arrays for computing the eigenvalue/singular value decomposition of Hermitian/arbitrary matrices, and three specific Q transformations that are needed in such arrays are identified. Issues related to the use of CORDIC for complex arithmetic are addressed, and implementations in both conventional (nonredundant) CORDIC and redundant and online modifications to CORDIC are described. If the time to compute a CORDIC operation in nonredundant CORDIC is T/sub c/, the Q transformations identified here can be evaluated and/or applied in 2T/sub c/ using four CORDIC modules for maximum concurrency. In either case, 0.5 T/sub c/ is required to account for scale factor correction. It is shown that a Q transformation can be evaluated and/or applied in /spl ap/10n, where n is the desired bit-precision.<>
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