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Résolution systolique de systèmes linéaires denses. (French) Zbl 0577.65024
The authors propose two systolic arrays using, instead of the usual triangularisation, the Jordan diagonalisation which appears to be well- suited for parallel computation.
Reviewer: A.de Castro

65F05 Direct numerical methods for linear systems and matrix inversion
68N25 Theory of operating systems
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[1] H. M. AHMED, J. M. DELOSME, M. MORF, Highly concurrent Computing structures for matrix arithmetic and signal processing. Computer magazine> January 1982, pp. 65-82.
[2] F. ANDRÉ, P. FRISON, P. QUINTON, Algorithmes systoliques : de la théorie à la pratique, Rapport de Recherche INRIA n^\circ 214, 1983.
[3] A. BOSSAVIT, Préface des actes du colloque AFCET-GAMNI-ISINA, 17-18 mars 1983, Paris, Bulletin de la direction des études et recherches EDF, série C, vol 1, 1983. Zbl0586.68004 · Zbl 0586.68004
[4] M. COSNARD, Y. ROBERT, Complexité de la factorisation QR en parallèle, C. R. Acad. Se. Paris, t. 297, Série I, pp. 137-139 (septembre 1983), Zbl0529.68019 MR720927 · Zbl 0529.68019
[5] J. M. DELOSME, Algoritkms for finite shift-rank processes, Ph. D., Technical Report M735-22, September 1982, Stanford Electronics Laboratories. · Zbl 0538.65019
[6] M. FLYNN, Some computer organisations and their effectiveness, IEEE Trans. on Computers C21, 9 (1972), pp. 948-960. Zbl0241.68020 · Zbl 0241.68020 · doi:10.1109/TC.1972.5009071
[7] M. J. FOSTER, H. T. KUNG, The design of special-purpose VLSI chips, IEEE Com-puter 13, 1 (January 1980), pp. 26-40,
[8] W. M. GENTLEMAN, Least squares computation by Givens transformations without square roots, J. Inst. Math. Appl. 12 (1973) pp. 329-336. Zbl0289.65020 MR329233 · Zbl 0289.65020 · doi:10.1093/imamat/12.3.329
[9] W. M. GENTLEMAN, H. T. KUNG, Matrix triangularisation by systolic arrays, Proc. SPIE 298, Real-time Signal Processing IV, San Diego, California, 1981.
[10] D. HELLER, A survey of parallel algorithms in numerical linear algebra, Siam Review 20, pp. 740-777, 1978. Zbl0408.68033 MR508381 · Zbl 0408.68033 · doi:10.1137/1020096
[11] D. HELLER, I. IPSEN, Systolic networks for orthogonal equivalence transformations and their applications, Proc. 1982Conf. Advanced Research in VLSI, pp. 113-122, MIT 1982.
[12] H. T. KUNG, Why systolic architectures, IEEE Computer 15, 1 (January 1982), pp. 37-46.
[13] H. T. KUNG, C. E. LEISERSON, Systolic Arrays for (VLSI), in the proceedings of the Symposium on sparse matrix computations and their applications, Knoxville, 1978. Zbl0404.68037 MR566379 · Zbl 0404.68037
[14] R. E. LORD, S. P. KOWALIK, S. P. KUMAR, Solving linear algebraic equations on an MIMD computer, J. ACM 30 (1), pp. 103-117, 1983. Zbl0502.65017 MR694482 · Zbl 0502.65017 · doi:10.1145/322358.322366
[15] L. MELKEMI, M. TCHUENTE, Systolic arrays for connectivity and triangularisation problems, to appear in Proc, < Dynamical Systems and Cellular Automata > , J. Demongeot, E. Coles et M. Tchuente eds., Academic Press, 1985. MR818534
[16] A. SAMEH, Numerical parallel algorithms - a survey, in < High Speed Computer and Algorithm Organization > , D. Kuck, D. Lawrie and A. Sameh eds., pp. 207-228, Academic Press, 1977.
[17] A. SAMEH, D. KUCK, On stable parallel System solvers, J. ACM 25 (1), pp. 81-91, 1978. Zbl0364.68051 MR483334 · Zbl 0364.68051 · doi:10.1145/322047.322054
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