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Using Strassen’s matrix multiplication in high performance solution of linear systems. (English) Zbl 0874.65015
Summary: Performance characteristics of dense and structured blocked linear system solvers are studied when Strassen’s matrix multiplication is used in the update step. Results of experiments on a multiprocessor Cray Y-MP are presented and discussed.

MSC:
65F05 Direct numerical methods for linear systems and matrix inversion
65F30 Other matrix algorithms (MSC2010)
Software:
ARCELO; COLROW; LAPACK
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References:
[1] Strassen, V., Gaussian elimination is not optimal, Numerical mathematics, 13, 354-356, (1969) · Zbl 0185.40101
[2] Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D., LAPACK User’s guide, (1993), SIAM Philadelphia · Zbl 0843.65018
[3] Dayde, M.J.; Duff, I.S., Level 3 BLAS in LU factorization on cray-2, ETA-10P and IBM 3090-200/VF, The international journal of supercomputer applications, 3, 40-70, (1989)
[4] Bailey, D.H.; Lee, K.; Simon, H.D., Using Strassen’s algorithm to accelerate the solution of linear systems, The journal of supercomputing, 4, 357-371, (1990) · Zbl 1215.65049
[5] Paprzycki, M., Comparison of Gaussian elimination algorithms on a cray Y-MP, Lin. alg. and appl., 172, 57-69, (1992) · Zbl 0756.65039
[6] Higham, N.J., Exploiting fast matrix multiplication within the level 3 BLAS, ACM trans. on math. soft., 16, 352-368, (1990) · Zbl 0900.65118
[7] Paprzycki, M.; Cyphers, C., Multiplying matrices on the cray—practical considerations, CHPC newsletter, 6, 77-82, (1991)
[8] Paprzycki, M., Parallel matrix multiplication—can we learn anything new?, CHPC newsletter, 7, 55-59, (1992)
[9] van de Geijn, R.A., LINPACK benchmark on the intel touchstone GAMMA and DELTA machines, ()
[10] Diaz, J.C.; Fairweather, G.; Keast, P., FORTRAN packages for solving certain almost block diagonal linear systems by modified alternative row and column elimination, ACM trans. on math. software, 9, 359-375, (1983) · Zbl 0516.65013
[11] Cyphers, C.; Paprzycki, M.; Gladwell, I., A level 3 BLAS based solver for almost block diagonal systems, () · Zbl 0892.65018
[12] Paprzycki, M.; Gladwell, I., Solving almost block diagonal systems using level 3 BLAS, (), 52-62 · Zbl 0788.65032
[13] Gladwell, I.; Paprzycki, M., Parallel solution of almost block diagonal systems using level 3 BLAS, J. of comp. and appl. math., 45, 181-189, (1993) · Zbl 0780.65017
[14] Karageorghis, A., The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method, Comp. meth. in appl. mech. and eng., 100, 339-358, (1992) · Zbl 0825.76607
[15] C. Cyphers, M. Paprzycki and A. Karageorghis, High performance solution of partial differential equations discretized using a Chebyshev spectral collocation method, J. Comp. Apl. Math. (to appear). · Zbl 0854.65101
[16] Paprzycki, M.; Irwin, N.; Hodges, P.E., Using BLAS in the estimation of nonlinear, non-Gaussian state-space models, (), 332-342
[17] Brown, J.A., A transform approach to fast matrix multiplication, ()
[18] Chou, C.C.; Deng, Y.; Li, G.; Wang, Y., Parallelizing Strassen’s method for matrix multiplication on distributed-memory MIMD computers, The university at stony brook technical report, (1994), SUNYSB-AMS-93-17
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