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References

1
J. Dongarra, J. Bunch, C. Moler, and G. W. Stewart, LINPACK User's Guide (SIAM, Philadelphia, PA, 1979).

2
E. Anderson et al., LAPACK Users' Guide, Release 1.0 (SIAM, Philadelphia, 1992), 235 pages.

3
J. Demmel, M. Heath, and H. van der Vorst, in Acta Numerica, volume 2, edited by A. Iserles (Cambridge University Press, ADDRESS, 1993).

4
G. Golub and C. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins University Press, Baltimore, MD, 1989).

5
D. Watkins, Fundamentals of Matrix Computations (Wiley, ADDRESS, 1991).

6
J. Demmel, Berkeley Lecture Notes in Numerical Linear Algebra, Mathematics Department, University of California, 1993, 215 pages.

7
J. Dongarra and E. Grosse, Communications of the ACM 30, 403 (1987).

8
J. Dongarra, I. Duff, D. Sorensen, and H. van der Vorst, Solving linear systems on vector and shared memory computers (SIAM, Philadelphia, PA, 1991), 256 pages.

9
K. Gallivan et al., Parallel algorithms for matrix computations (SIAM, Philadelphia, PA, 1990).

10
C. Lawson, R. Hanson, D. Kincaid, and F. Krogh, ACM Trans. Math. Soft. 5, 308 (1979).

11
J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson, ACM Trans. Math. Soft. 14, 1 (1988).

12
J. Dongarra, J. Du Croz, I. Duff, and S. Hammarling, ACM Trans. Math. Soft. 16, 1 (1990).

13
B. T. Smith et al., Matrix Eigensystem Routines -- EISPACK Guide, Vol. 6 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1976).

14
B. S. Garbow, J. M. Boyle, J. J. Dongarra, and C. B. Moler, Matrix Eigensystem Routines -- EISPACK Guide Extension, Vol. 51 of Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1977).

15
X. Hong and H. T. Kung, in Proceedings of the 13th Symposium on the Theory of Computing (ACM, ADDRESS, 1981), pp. 326--334.

16
S. L. Johnsson, private communication, 1990.

17
E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms (Computer Science Press, Potomac, MD, 1978).

18
D. H. Bailey, K. Lee, and H. D. Simon, J. Supercomputing 4, 97 (1991).

19
J. Demmel and N. J. Higham, ACM Trans. Math. Soft. 18, 274 (1992).

20
L. Cannon, Ph.D. thesis, Montana State University, Bozeman, MN, 1969.

21
G. Fox et al., Solving problems on concurrent processors, v. I (Prentice Hall, ADDRESS, 1988).

22
C. T. Ho, Ph.D. thesis, Yale University, 1990.

23
S. L. Johnsson, J. of Parallel and Distributed Computing 4, 133 (1987).

24
E. Dekel, D. Nassimi, and S. Sahni, SIAM J. Comput. 10, 657 (1981).

25
C. T. Ho, S. L. Johnsson, and A. Edelman, in The Sixth Distributed Memory Computing Conference Proceedings (IEEE Computer Society Press, ADDRESS, 1991), pp. 447--451.

26
G. Fox et al., Computer Science Department Report CRPC-TR90079, Rice University, Houston, TX (unpublished).

27
High Performance Fortran, documentation available via anonymous ftp from titan.cs.rice.edu in directory public/HPFF, 1991.

28
E. Van de Velde, caltech, Pasadena, CA (unpublished).

29
E. Anderson and J. Dongarra, Computer Science Dept. Technical Report CS-90-103, University of Tennessee, Knoxville (unpublished), (LAPACK Working Note #19).

30
Y. Robert, The impact of vector and parallel architectures on the Gaussian elimination algorithm (Wiley, ADDRESS, 1990).

31
J. Dongarra and S. Ostrouchov, Computer Science Dept. Technical Report CS-90-115, University of Tennessee, Knoxville (unpublished), (LAPACK Working Note #24).

32
J. Dongarra and R. van de Geijn, Computer Science Dept. Technical Report CS-91-138, University of Tennessee, Knoxville (unpublished), (LAPACK Working Note #37).

33
S. Eisenstat, M. Heath, C. Henkel, and C. Romine, SIAM J. Sci. Stat. Comput. 9, 589 (1988).

34
M. Heath and C. Romine, SIAM J. Sci. Stat. Comput. 9, 558 (1988).

35
G. Li and T. Coleman, SIAM J. Sci. Stat. Comput. 9, 485 (1988).

36
C. Romine and J. Ortega, Parallel Computing 6, 109 (1988).

37
J. Du Croz, P. J. D. Mayes, and G. Radicati di Brozolo, Computer Science Dept. Technical Report CS-90-109, University of Tennessee, Knoxville (unpublished), (LAPACK Working Note #21.

38
J. Ortega, Introduction to Parallel and Vector Solution of Linear Systems (Plenum Press, ADDRESS, 1988).

39
I. Babuska, SIAM J. Numer. Anal. 9, 53 (1972).

40
H. A. van der Vorst, Parallel Computing 5, 303 (1987).

41
H. Stone, J. Assoc. Comput. Mach. 20, 27 (1973).

42
P. Dubois and G. Rodrigue, in High speed computer and algorithm organization, edited by D. J. Kuck and A. H. Sameh (Academic Press, New York, 1977).

43
J. J. Lambiotte and R. G. Voigt, Technical report, ICASE-NASA Langley Research Center, Hampton, VA (unpublished).

44
D. Heller, SIAM J. Numer. Anal. 13, 484 (1978).

45
P. P. N. de Groen, Appl. Num. Math. 8, 117 (1991).

46
J. J. F. M. Schlichting and H. A. van der Vorst, Technical Report No. NM-R8725, CWI, Amsterdam, the Netherlands (unpublished).

47
S. C. Chen, D. J. Kuck, and A. H. Sameh, ACM Trans. Math. Software 4, 270 (1978).

48
H. H. Wang, ACM Trans. Math. Software 7, 170 (1981).

49
H. A. van der Vorst and K. Dekker, SIAM J. Sci. Stat. Comput. 10, 27 (1989).

50
P. H. Michielse and H. A. van der Vorst, Parallel Computing 7, 87 (1988).

51
H. A. van der Vorst, Future Generation Computer Systems 4, 285 (1989).

52
U. Meier, Parallel Comput. 2, 33 (1985).

53
V. Mehrmann, Technical Report No. Bericht Nr. 68, Inst. fuer Geometrie und Prakt. Math., Aachen (unpublished).

54
M. Heath, E. Ng, and B. Peyton, SIAM Review 33, 420 (1991).

55
I. Duff, A. Erisman, and J. Reid, Direct Methods for Sparse Matrices (Oxford University Press, Oxford, England, 1986).

56
A. George and J. Liu, Computer Solution of Large Sparse Positive Definite Systems (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1981).

57
J. Liu, SIAM J. Matrix Anal. Appl. 11, 134 (1990).

58
B. Irons, Internat. J. Numer. Meth. Engrg. 2, 5 (1970).

59
C. Ashcraft et al., Internat. J. Supercomp. Appl 1, 10 (1987).

60
E. Rothberg and A. Gupta, Technical Report No. STAN-CS-89-1286, Stanford University, Stanford, California (unpublished).

61
J. Liu, Parallel Computing 3, 327 (1986).

62
J. Jess and H. Kees, IEEE Trans. Comput. C-31, 231 (1982).

63
J. Lewis, B. Peyton, and A. Pothen, SIAM J. Sci. Stat. Comput. 10, 1156 (1989).

64
J. Liu, Parallel Computing 11, 73 (1989).

65
A. George and J. Liu, SIAM Review 31, 1 (1989).

66
A. George, SIAM J. Num. Anal. 10, 345 (1973).

67
A. George, M. Heath, J. Liu, and E. Ng, Internat. J. Parallel Programming 15, 309 (1986).

68
A. George, M. Heath, J. Liu, and E. Ng, J. Comp. Appl. Math. 27, 129 (1989).

69
A. George, M. Heath, J. Liu, and E. Ng, SIAM J. Sci. Stat. Comput. 9, 327 (1988).

70
A. George, J. Liu, and E. Ng, Parallel Computing 10, 287 (1989).

71
M. Mu and J. Rice, SIAM J. Sci. Stat. Comput. 13, 826 (1992).

72
E. Zmijewski, Technical Report No. TRCS89-18, Department of Computer Science, University of California, Santa Barbara, CA (unpublished).

73
C. Ashcraft, S. Eisenstat, and J. Liu, SIAM J. Sci. Stat. Comput. 11, 593 (1990).

74
R. Benner, G. Montry, and G. Weigand, Internat. J. Supercomp. Appl 1, 26 (1987).

75
I. Duff, Parallel Computing 3, 193 (1986).

76
J. Gilbert and R. Schreiber, SIAM J. Sci. Stat. Comput. 13, 1151 (1992).

77
R. Lucas, W. Blank, and J. Tieman, IEEE Trans. Computer Aided Design CAD-6, 981 (1987).

78
C. Ashcraft, S. Eisenstat, J. Liu, and A. Sherman, Technical Report No. YALEU/DCS/RR-810, Dept. of Computer Science, Yale University, New Haven, CT (unpublished).

79
R. Freund, G. Golub, and N. Nachtigal, in Acta Numerica 1992, edited by A. Iserles (Cambridge University Press, ADDRESS, 1992), pp. 57--100.

80
E. de Sturler, Technical Report No. 91-85, Delft University of Technology, Delft (unpublished).

81
C. Pommerell, Ph.D. thesis, Swiss Federal Institute of Technology, Zürich, 1992.

82
J. A. Meijerink and H. A. van der Vorst, Math.Comp. 31, 148 (1977).

83
J. A. Meijerink and H. A. van der Vorst, J. Comp. Phys. 44, 134 (1981).

84
C. Ashcraft and R. Grimes, SIAM J. Sci. Stat. Comput. 9, 122 (1988).

85
H. A. van der Vorst, SIAM J. Sci. Statist. Comput. 10, 1174 (1989).

86
H. A. van der Vorst, in Proc. of the fifth Int.Symp. on Numer. Methods in Eng., edited by R. Gruber, J. Periaux, and R. P. Shaw (PUBLISHER, ADDRESS, 1989), vol 1.

87
J. J. F. M. Schlichting and H. A. van der Vorst, Journal of Comp. and Appl. Math. 27, 323 (1989).

88
I. S. Duff and G. A. Meurant, BIT 29, 635 (1989).

89
H. A. van der Vorst, J. Comp. and Appl. Math. 18, 249 (1987).

90
S. Doi, Appl. Num. Math. 7, 417 (1991).

91
M. K. Seager, Parallel Computing 3, 35 (1986).

92
G. Radicati di Brozolo and Y. Robert, Technical Report No. 681-M, IMAG/TIM3, Grenoble (unpublished).

93
H. Berryman, J. Saltz, W. Gropp, and R. Mirchandaney, Technical Report No. 89-54, NASA Langley Research Center, ICASE, Hampton, VA (unpublished).

94
Y. Saad, SIAM J. Sci. Stat. Comput. 6, 865 (1985).

95
N. K. Madsen, G. H. Rodrigue, and J. I. Karush, Inform. Process.Lett. 5, 41 (1976).

96
H. A. van der Vorst, SIAM J. Sci. Stat. Comput. 3, 86 (1982).

97
M. R. Hestenes and E. Stiefel, J. Res. Natl. Bur. Stand. 49, 409 (1954).

98
A. T. Chronopoulos and C. W. Gear, J. on Comp. and Appl. Math. 25, 153 (1989).

99
G. Meurant, Technical Report No. LBL-18023, University of California, Berkeley, CA (unpublished).

100
G. Meurant, BIT 24, 623 (1984).

101
H. A. van der Vorst, Parallel Computing 3, 49 (1986).

102
A. T. Chronopoulos, in Supercomputing '91 (IEEE Computer Society Press, Los Alamitos, CA, 1991), pp. 578--587.

103
Y. Saad, Technical report, RIACS, Moffett Field, CA (unpublished).

104
A. T. Chronopoulos and S. K. Kim, Technical Report No. 90/43R, UMSI, Minneapolis (unpublished).

105
E. D'Azevedo and C. Romine, Technical Report ORNL/TM-12192, Oak Ridge National Laboratory (unpublished).

106
V. Eijkhout, Compute Science Dept. Technical Report CS-92-170, University of Tennessee at Knoxville (unpublished).

107
Y. Saad and M. H. Schultz, SIAM J. Sci. Statist. Comput. 7, 856 (1986).

108
Y. Saad and M. H. Schultz, Math. of Comp. 44, 417 (1985).

109
H. F. Walker, SIAM J. Sci. Stat. Comp. 9, 152 (1988).

110
H. A. van der Vorst and C. Vuik, Technical Report No. 91-80, Delft University of Technology, Faculty of Tech. Math. (unpublished).

111
Z. Bai, D. Hu, and L. Reichel, Technical Report No. 91-03, University of Kentucky (unpublished).

112
D. Calvetti, J. Petersen, and L. Reichel, Technical Report No. ICM-9110-6, Institute for Computational Mathematics, Kent, OH (unpublished).

113
W. W. Hager, SIAM J. Sci. Stat. Comput. 5, 311 (1984).

114
N. J. Higham, SIAM Review 29, 575 (1987).

115
N. J. Higham, SIAM J. Sci. Stat. Comput. 11, 804 (1990).