A ScaLAPACK-style algorithm for reducing a regular matrix pair to block Hessenberg-triangular form
A parallel algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-triangular form is presented. It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations. Moreover, this LAPACK-style algorithm is straightforwardly extended to a parallel algorithm for a rectangular 2D processor grid using parallel kernels from ScaLAPACK. A hierarchical performance model is derived and used for algorithm analysis and selection of optimal blocking parameters and grid sizes.
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- 3.K. Dackland and B. Kågström. Reduction of a Regular Matrix Pair (A, B) to Block Hessenberg-Trinngular Form. In Dongarra et.al., editors, Applied Parallel Computing: Computations in Physics, Chemistry and Engineering Scienc, pages 125–133, Berlin, 1995. Springer-Verlag. Lecture Notes in Computer Science, Vol. 1041, Proceedings, Lyngby, Denmark.Google Scholar
- 4.K. Dackland and B. Kågström. An Hierarchical Approach for Performance Analysis of ScaLAPACK-based Routines Using the Distributed Linear Algebra Machine. In Dongarra et.al., editors, Applied Parallel Computing: Computations in Physics, Chemistry and Engineering Science, pages 187–195, Berlin, 1996. Springer-Verlag. Lecture Notes in Computer Science, Vol. 1184, Proceedings, Lyngby, Denmark.Google Scholar
- 5.K. Dackland. Parallel Reduction of a Regular Matrix Pair to Block Hessenberg-Triangular Form-Algorithm Design and Performance Modeling. Report UMINF-98.09, Department of Computing Science, Umeå University, S-901 87 Umeå, 1998.Google Scholar
- 7.G. H. Golub and C. F. Van Loan. Matrix Computations, Second Edition, The John Hopkins University Press, Baltimore, Maryland, 1989.Google Scholar