Pub Date : 1996-06-01DOI: 10.1142/S0129053396000112
J. Barlow, P. Yoon
A fully parallel algorithm for updating and downdating the singular value decompositions (SVD’s) of an m-by-n(m≥n) matrix A is described. The algorithm uses similar chasing techniques for modifying the SVD’s described in [3], but requires fewer plane rotations, and can be implemented almost identically for both updating and downdating. Both cyclic and consecutive storage schemes are considered in parallel implementation. We show that the latter scheme outperforms the former on a distributed memory MIMD multiprocessor. We present the experimental results on the 32-node Connection Machine (CM-5).
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Pub Date : 1995-12-01DOI: 10.1142/S0129053395000300
Sun Xian-he, D. Ronald
A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study has been conducted to provide a simple truncation formula. Experimental results have been measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers.
{"title":"A Parallel Prefix Algorithm for Almost Toeplitz Tridiagonal Systems","authors":"Sun Xian-he, D. Ronald","doi":"10.1142/S0129053395000300","DOIUrl":"https://doi.org/10.1142/S0129053395000300","url":null,"abstract":"A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study has been conducted to provide a simple truncation formula. Experimental results have been measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers.","PeriodicalId":165154,"journal":{"name":"International journal of high speed computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121180427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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