Abstract
A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-triangular form (H,T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-triangular form (H rT), where H r is upper r-Hessenberg with r > 1 subdiagonals and T is upper triangular. In stage two, the desired upper Hessenberg-triangular form is computed using two-sided Givens rotations. Performance results for the ScaLAPACK-style implementations show that the parallel algorithms can be used to solve large scale problems effectively.
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Adlerborn, B., Dackland, K., Kågström, B. (2001). Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form. In: Sørevik, T., Manne, F., Gebremedhin, A.H., Moe, R. (eds) Applied Parallel Computing. New Paradigms for HPC in Industry and Academia. PARA 2000. Lecture Notes in Computer Science, vol 1947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70734-4_13
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DOI: https://doi.org/10.1007/3-540-70734-4_13
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