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Parallel and blocked algorithms for reduction of a regular matrix pair to hessenberg-triangular and generalized Schur forms. (English) Zbl 1048.65508
Fagerholm, Juha (ed.) et al., Applied parallel computing. Advanced scientific computing. 6th international conference, PARA 2002, Espoo, Finland, June 15–18, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43786-X). Lect. Notes Comput. Sci. 2367, 319-328 (2002).
Summary: A parallel three-stage algorithm for reduction of a regular matrix pair $$(A, B)$$ to generalized Schur from $$(S, T)$$ is presented. The first two stages transform $$(A,B)$$ to upper Hessenberg-triangular form $$(H,T)$$ using orthogonal equivalence transformations. The third stage iteratively reduces the matrix in $$(H,T)$$ form to generalized Schur form. Algorithm and implementation issues regarding the single-/double-shift QZ algorithm are discussed. We also describe multishift strategies to enhance the performance in blocked as well as in parallell variants of the QZ method.
For the entire collection see [Zbl 0997.68670].

##### MSC:
 65Y05 Parallel numerical computation 65F30 Other matrix algorithms (MSC2010)
##### Software:
LAPACK; PETSc; P-SPARSLIB; QMRPACK; ScaLAPACK
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