Name
Abstract | ||
|---|---|---|
In this paper we report an effective parallelisation of the Householder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like αN 3 /P+βN 2 log 2 (P) and the QL algorithm like γN 2 + δN 3 / P as the number of processors P is increased for fixed problem size. The constant parameters α , β , γ and δ are obtained empirically. When the eigenvalues only are required the Householder method scales as above while the QL algorithm remains sequential. The code is implemented in c in conjunction with the message passing interface (MPI) libraries and verified on a sixteen node IBM SP2 and for real matrices that occur in the simulation of properties of crystaline materials. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1016/S0167-8191(98)00116-1 | Parallel Computing |
Keywords | Field | DocType |
linear algebra,householder,householder-ql matrix diagonalisation algorithm,matrix diagonalisation,parallel algorithms,efficient parallel version,ql,message passing interface,eigenvalues,symmetric matrix,parallel algorithm | Linear algebra,Parallel algorithm,2 × 2 real matrices,Computer science,Matrix (mathematics),Parallel computing,Algorithm,Symmetric matrix,Theoretical computer science,Message Passing Interface,Householder's method,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
25 | 3 | Parallel Computing |
Citations | PageRank | References |
3 | 0.58 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. S. REEVE | 1 | 18 | 5.17 |
| Michael T. Heath | 2 | 366 | 73.58 |