Block Gauss Reduction to Hessenberg Form
| Autor: | Augustin A. Dubrulle |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Numerical linear algebra
Gauss MathematicsofComputing_NUMERICALANALYSIS Block matrix computer.software_genre Householder transformation Algebra Matrix (mathematics) Elementary matrix ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics Gauss–Seidel method Householder's method computer Mathematics |
| Zdroj: | SIAM Journal on Scientific and Statistical Computing. 12:1245-1253 |
| ISSN: | 2168-3417 0196-5204 |
| Popis: | The latest developments in matrix software generally confine the block methods based on stabilized elementary (Gauss) transformations to the solution of linear equations, in a concern for numerical stability. For example, LAPACK relies entirely on Householder methods for the solution of standard eigenvalue problems, including the reduction to Hessenberg form. There is, however, a wide range of problems in practice for which the Gauss reduction, more economical of computation, is safe and quite comparable to its Householder alternative for accuracy of the computed eigenvalues. In this paper, a block version of the Gauss reduction is derived from the serial method by bundling sequences of stabilized elementary matrices into single operators amenable to implementation with high-level BLAB. Results of experiments conducted with an IBM 3090 VF model E (one processor) for random matrices include details of FORTRAN implementation and a performance comparison with a Householder block algorithm. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|