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Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling. (English) Zbl 1382.65095
MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A18 Eigenvalues, singular values, and eigenvectors
Software:
ScaLAPACK
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References:
[1] B. Adlerborn, K. Dackland, and B. Kågström, Parallel two-stage reduction of a regular matrix pair to Hessenberg-Triangular form, in Applied Parallel Computing, PARA 2000, T. Sørevik, F. Manne, A. H. Gebremedhin, and R. Moe, eds., Lecture Notes in Comput. Sci. 1947, Springer, Berlin, 2000, pp. 92–102.
[2] B. Adlerborn, K. Dackland, and B. Kågström, Parallel and blocked algorithms for reduction of a regular matrix pair to Hessenberg-Triangular and generalized Schur forms, in Applied Parallel Computing, PARA 2002, J. Fagerholm, J. Haataja, J. Järvinen, M. Lyly, P. R\raback, and V. Savolainen, eds., Lecture Notes in Comput. Sci. 2367, Springer, Berlin, 2002, pp. 319–328. · Zbl 1048.65508
[3] B. Adlerborn, B. Kågström, and D. Kressner, Parallel variants of the multishift QZ algorithm with advanced deflation techniques, in Applied Parallel Computing, PARA 2006, B. Kågström, E. Elmroth, J. Dongarra, and J. Waśniewski, eds., Lecture Notes in Comput. Sci. 4699, Springer, Berlin, 2006, pp. 117–126.
[4] B. Adlerborn, B. Kågström, and D. Kressner, A parallel QZ algorithm for distributed memory HPC systems, SIAM J. Sci. Comput., 36 (2014), pp. C480–C503. · Zbl 1307.65039
[5] C. Bischof, A Summary of Block Schemes for Reducing a General Matrix to Hessenberg Form, Technical report ANL/MSC-TM-175, Argonne National Laboratory, 1993.
[6] C. H. Bischof and C. F. Van Loan, The \({W}{Y}\) representation for products of Householder matrices, SIAM J. Sci. Statist. Comput., 8 (1987), pp. S2–S13. · Zbl 0628.65033
[7] L. S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. W. Demmel, I. Dhillon, J. J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley, ScaLAPACK Users’ Guide, SIAM, Philadelphia, 1997. · Zbl 0886.65022
[8] K. Dackland and B. Kågström, A ScaLAPACK-style algorithm for reducing a regular matrix pair to block Hessenberg-Triangular form, in Applied Parallel Computing, PARA 1998, B. Kågström, J. Dongarra, E. Elmroth, and J. Waśniewski, eds., Lecture Notes in Comput. Sci. 1541, Springer, Berlin, 1998, pp. 95–103.
[9] K. Dackland and B. Kågström, Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form, ACM Trans. Math. Software, 25 (1999), pp. 425–454. · Zbl 0962.65041
[10] B. Kågström and D. Kressner, Multishift variants of the QZ algorithm with aggressive early deflation, SIAM J. Matrix Anal. Appl., 29 (2006), pp. 199–227. · Zbl 1137.65017
[11] B. Kågström, D. Kressner, E. S. Quintana-Ortí, and G. Quintana-Ortí, Blocked algorithms for the reduction to Hessenberg-triangular form revisited, BIT, 48 (2008), pp. 563–584. · Zbl 1157.65348
[12] B. Lang, Using level 3 BLAS in rotation-based algorithms, SIAM J. Sci. Comput., 19 (1998), pp. 626–634. · Zbl 0912.65032
[13] C. B. Moler and G. W. Stewart, An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal., 10 (1973), pp. 241–256. · Zbl 0253.65019
[14] R. C. Ward, The combination shift QZ algorithm, SIAM J. Numer. Anal., 12 (1975), pp. 835–853. · Zbl 0342.65022
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