Paper Info
Title
Solving tridiagonal systems of linear equations on the IBM 3090 VF
Abstract
Cyclic reduction, originally proposed by Hockney and Golub, is the most popular algorithm for solving tridiagonal linear systems on SIMD-type computers like CRAY-1 or CDC CYBER 205. That algorithm seems to be the adequate one for the IBM 3090 VF (uni-processor), too, although the overall expected speedup over Gaussian elimination, specialized for tridiagonal systems, is not as high as for the CRAY-1 or the CYBER 205. That is because the excellent scalar speed of the IBM 3090 makes its vector-to-scalar speed ratio relatively moderate. The idea of the cyclic reduction algorithm can be generalized and modified in various directions. A polyalgorithm can be derived which takes into account much better the given architecture of the IBM 3090 VF than the ‘pure’ cyclic reduction algorithm as described for instance by Kershaw. This is mainly achieved by introducing more locality into the formulae. For large systems of equations the well-known cache problems are prevented.
Year
DOI
Venue
1988
10.1016/0167-8191(88)90141-X
PARALLEL COMPUTING
Keywords
Field
DocType
cyclic reduction,linear algebra,tridiagonal linear systems,vector computers,linear equations
Tridiagonal matrix,Linear algebra,System of linear equations,Computer science,Cache,Parallel computing,Theoretical computer science,Gaussian elimination,Tridiagonal matrix algorithm,Cyclic reduction,Speedup
Journal
Volume
Issue
ISSN
8
1-3
0167-8191
Citations 
PageRank 
References 
5
1.56
1
Authors
1
Name
Order
Citations
PageRank
Richard Reuter152.57