Abstract
An algorithm for reduction of a regular matrix pair (A, B) to block Hessenberg-triangular form is presented. This condensed form Q T (A,B)Z = (H,T), where H and T axe block upper Hessenberg and upper triangular, respectively, and Q and Z orthogonal, may serve as a first step in the solution of the generalized eigenvalue problem Ax = λBx. It is shown how an elementwise algorithm can be reorganized in terms of blocked factorizations and higher level BLAS operations. Several ways to annihilate elements are compared. Specifically, the use of Givens rotations, Householder transformations, and combinations of the two. Performance results of the different variants are presented and compared to the LAPACK implementation DGGHRD, which indeed is unblocked.
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© 1996 Springer-Verlag Berlin Heidelberg
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Dackland, K., Kågström, B. (1996). Reduction of a regular matrix pair (A, B) to block Hessenberg-triangular form. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing Computations in Physics, Chemistry and Engineering Science. PARA 1995. Lecture Notes in Computer Science, vol 1041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60902-4_15
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DOI: https://doi.org/10.1007/3-540-60902-4_15
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