Abstract
A new cache-efficient algorithm for reduction from block Hessenberg form to Hessenberg form is presented and evaluated. The algorithm targets parallel computers with shared memory. One level of look-ahead in combination with a dynamic load-balancing scheme significantly reduces the idle time and allows the use of coarse-grained tasks. The coarse tasks lead to high-performance computations on each processor/core. Speedups close to 13 over the sequential unblocked algorithm have been observed on a dual quad-core machine using one thread per core.
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References
Adlerborn, B., Dackland, K., Kågström, B.: Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form. In: Sørvik, T., et al. (eds.) PARA 2000. LNCS, vol. 1947, pp. 92–102. Springer, Heidelberg (2001)
Bischof, C.H., Lang, B., Sun, X.: A framework for symmetric band reduction. ACM Trans. Math. Software 26(4), 581–601 (2000)
Dackland, K., Kågström, B.: Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form. ACM Trans. Math. Software 25(4), 425–454 (1999)
Kågström, B., Kressner, D., Quintana-Orti, E., Quintana-Orti, G.: Blocked algorithms for the reduction to Hessenberg-triangular form revisited. BIT Numerical Mathematics 48(1), 563–584 (2008)
Ltaief, H., Kurzak, J., Dongarra, J.J., Badia, R.M.: Scheduling two-sided transformations using tile algorithms on multicore architectures. Scientific Programming 18(1), 35–50 (2010)
Mohanty, S.: I/O Efficient Algorithms for Matrix Computations. Ph.D. thesis, Indian Institute of Technology Guwahati (2009)
Murata, K., Horikoshi, K.: A new method for the tridiagonalization of the symmetric band matrix. Information Processing in Japan 15, 108–112 (1975)
Rutishauser, H.: On Jacobi rotation patterns. In: Proc. Sympos. Appl. Math., vol. XV, pp. 219–239. Amer. Math. Soc., Providence (1963)
Tomov, S., Dongarra, J.J.: Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing. Tech. Rep. UT-CS-09-642, University of Tennessee Computer Science (May 2009); also as LAPACK Working Note 219
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Karlsson, L., Kågström, B. (2012). Efficient Reduction from Block Hessenberg Form to Hessenberg Form Using Shared Memory. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_26
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DOI: https://doi.org/10.1007/978-3-642-28145-7_26
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