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T.A. Davis, E.S. Davidson, "Pairwise Reduction for the Direct, Parallel Solution of Sparse, Unsymmetric Sets of Linear Equations," IEEE Transactions on Computers, vol. 37, no. 12, pp. 16481654, December, 1988.  
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@article{ 10.1109/12.9742, author = {T.A. Davis and E.S. Davidson}, title = {Pairwise Reduction for the Direct, Parallel Solution of Sparse, Unsymmetric Sets of Linear Equations}, journal ={IEEE Transactions on Computers}, volume = {37}, number = {12}, issn = {00189340}, year = {1988}, pages = {16481654}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.9742}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Pairwise Reduction for the Direct, Parallel Solution of Sparse, Unsymmetric Sets of Linear Equations IS  12 SN  00189340 SP1648 EP1654 EPD  16481654 A1  T.A. Davis, A1  E.S. Davidson, PY  1988 KW  pairwise reduction; parallel solution; sparse; unsymmetric sets; linear equations; concurrent computing; sharedmemory multiprocessor; pairwise solve; PSolve; linear algebra; parallel algorithms. VL  37 JA  IEEE Transactions on Computers ER   
[1] G. Alaghband, "Parallel pivoting combined with parallel reduction," ICASE Rep 8775, NASA Langley Res. Center. Hampton, VA, 1987.
[2] S. G. Abraham, "Reducing interprocessor communication in parallel architectures: System configuration and task assignment," CSRD Rep. 726, Center Supercomput. Res. Develop., Univ. Illinois, Urbana, IL, 1987.
[3] S. G. Abraham and T. A. Davis, "Blocking for parallel sparse linear system solvers," inProc. 1988 Int. Conf. Parallel Processing. Univ. Park, PA: Penn. State Univ. Press, 1988, vol. 1, pp. 166173.
[4] W. AbuSufah and A. D. Malony, "Vector processing on the Alliant FX/8 multiprocessor," inProc. 1986 Int. Conf. Parallel Processing. Univ. Park, PA: Penn. State Univ. Press, 1986, pp. 559566.
[5] Alliant Computer Systems Corp.,FX/Series Architecture Manual, Littleton, MA, 1986.
[6] P. E. Bjorstad, "A large scale, sparse, secondary storage, direct linear equation solver for structural analysis and its implementation on vector and parallel architectures,"Parallel Comput., vol. 5, pp. 312, 1987.
[7] D. A. Calahan, "Parallel solution of sparse simultaneous linear equations," inProc. 11th Allerton Conf. Circuits Syst. Theory, Univ. Illinois, Urbana, IL, 1973, pp. 729735.
[8] G. Dahlquist andÅ. Björk,Numerical Methods. Englewood Cliffs, NJ: PrenticeHall, 1974.
[9] A. K. Dave and I. S. Duff, "Sparse matrix calculations on the CRAY 2,"Parallel Comput., vol. 5, pp. 5564, 1987.
[10] T. A. Davis, "PSolve: A concurrent algorithm for solving sparse systems of linear equations," CSRD Rep. 612, Center Supercomput. Res. Develop., Univ. Illinois, Urbana, IL, 1986.
[11] T. A. Davis and E. S. Davidson, "PSolve: A concurrent algorithm for solving sparse systems of linear equations," inProc. 1987 Int. Conf. Parallel Processing. Univ. Park, PA: Penn. State Univ. Press, 1987, pp. 483490.
[12] E. W. Dijkstra, "Hierarchical ordering of sequential processes," inOperating Systems Techniques, C. A. R. Hoare and R. H. Perrott, Eds. New York: Academic, 1972, pp. 7293.
[13] I. S. Duff, R. Grimes, J. Lewis, and B. Poole, "Sparse matrix text problems,"SIGNUM Newsletter, vol. 17, p. 22, 1982.
[14] I. S. Duff and J. K. Reid, "Some design features of a sparse matrix code,"ACM Trans. Math. Software, vol. 5, pp. 1835, 1979.
[15] I. S. Duff and J. K. Reid, "The multifrontal solution of unsymmetric sets of linear equaions,"SIAM J. Sci. Stat. Comput., vol. 5, pp. 633641, 1984.
[16] I. S. Duff, "Parallel implementation of multifrontal schemes,"Parallel Comput., vol. 3, pp. 193204, 1986.
[17] S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, "The Yale sparse matrix package, II: The nonsymmetric codes," Rep. 114, Dep. Comput. Sci., Yale Univ., 1977.
[18] S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, "Yale sparse matrix package, I: The symmetric codes,"Int. J. Numer. Meth. Eng., vol. 18, pp. 11451151, 1982.
[19] A. George, M. T. Heath, J. W. H. Liu, and E. Ng, "Solution of sparse positive definite systems on a sharedmemory multiprocessor,"Int. J. Parallel Programming, vol. 15, no. 4, pp. 309325, 1986.
[20] A. George, M. T. Heath, E. Ng, and J. W. H. Liu, "Symbolic Cholesky factorization on a localmemory multiprocessor,"Parallel Comput., vol. 5, pp. 8595, 1987.
[21] R. W. Hockney and C. R. Jesshope,Parallel Computers. Bristol, England: Adam Hilger, 1981.
[22] J. W. Huang and O. Wing, "Optimal parallel triangulation of a sparse matrix,"IEEE Trans. Circuits Syst., vol. CAS26, pp. 726732, Sept. 1979.
[23] J. A. G. Jess and H. G. M. Kees, "A data structure for parallelL/Udecomposition,"IEEE Trans. Comput., vol. C31, pp. 231239, 1982.
[24] H. M. Markowitz, "The elimination form on the inverse and its application to linear programming,"Management Sci., vol. 3, pp. 255269, 1957.
[25] R. G. Melhem, "A modified frontal technique suitable for parallel systems,"SIAM J. Sci. Stat. Comput., vol. 9, pp. 289303, 1988.
[26] J. W. H. Liu, "Computational models and task scheduling for parallel sparse Cholesky factorization,"Parallel Comput., vol. 3, pp. 327 342, 1986.
[27] F. J. Peters, "Parallel pivoting algorithms for sparse symmetric matrices,"Parallel Comput., vol. 1, pp. 99110, 1984.
[28] A. H. Sameh, "On some parallel algorithms on a ring of processors,"Comput. Phys. Commun., vol. 37, pp. 159166, 1985.
[29] D. C. Sorenson, "Analysis of pairwise pivoting in Gaussian elimination,"IEEE Trans. Comput., vol. C34, pp. 274278, 1985.
[30] R. P. Tewarson,Sparse Matrices. New York: Academic, 1973.
[31] J. H. Wilkinson, "Error analysis of direct methods of matrix inversion,"J. ACM, vol. 8, pp. 281330, 1961.
[32] O. Wing and J. W. Huang, "A computation model of parallel solution of linear equations,"IEEE Trans. Comput., vol. C29, pp. 632638, 1980.