Abstract
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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References
M. Berry, J. Dongarra and Y. Kim. A Highly Parallel Algorithm for the Reduction of a Nonsymmetric Matrix to Block Upper-Hessenberg From. Parallel Computing, Vol. 21, No. 8, pp 1189–1212, 1995.
S. Blackford, J. Choi, A. Clearly, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petit, K. Stanley, D. Walker, and R.C. Whaley. ScaLAPACK Users’ Guide. SIAM Publications, Philadelphia, 1997.
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.
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.
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.
W. Enright and S. Serbin. A Note on the Efficient Solution of Matrix Pencil Systems. BIT, 18:276–281, 1978.
G. H. Golub and C. F. Van Loan. Matrix Computations, Second Edition, The John Hopkins University Press, Baltimore, Maryland, 1989.
C. B. Moler and G. W. Stewart. An Algorithm for Generalized Matrix Eigenvalue Problems. SIAM J. Num. Anal., 10:241–256, 1973.
R. Schreiber and C. Van Loan. A Storage Efficient WY Representation for Products of Householder Transformations. SIAM J. Sci. and Stat. Comp., 10:53–57, 1989.
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© 1998 Springer-Verlag Berlin Heidelberg
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Dackland, K., Kågström, B. (1998). A ScaLAPACK-style algorithm for reducing a regular matrix pair to block Hessenberg-triangular form. In: Kågström, B., Dongarra, J., Elmroth, E., Waśniewski, J. (eds) Applied Parallel Computing Large Scale Scientific and Industrial Problems. PARA 1998. Lecture Notes in Computer Science, vol 1541. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095325
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DOI: https://doi.org/10.1007/BFb0095325
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