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Updated triangular factors of the basis of maintain sparsity in the product form simplex method. (English) Zbl 0288.90048

MSC:
90C05 Linear programming
65K05 Numerical mathematical programming methods
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[1] R.H. Bartels, ”A numerical investigation of the simplex method,” Computer Science Department, Stanford University, Technical Report No. CS-104, July 31, 1968.
[2] R.H. Bartels and G.H. Golub, ”The simplex method of linear programming using LU decomposition,”Communications ACM 12 (1969) 266–268, 275–278. · Zbl 0181.19104
[3] E.M.L. Beale, ”Sparseness in linear programming,” in:Large sparse sets of linear equations, Ed. J.K. Reid (Academic Press, London, 1970) pp. 1–15.
[4] J.M. Bennett and D.R. Green, ”Updating the inverse or the triangular factors of a modified matrix,” Basser Computing Department, University of Sydney, Technical Report No. 42, April, 1966.
[5] R.K. Brayton, F.G. Gustavson and R.A. Willoughby, ”Some results on sparse matrices,” RC-2332, IBM Research Centre, Yorktown Heights, N.Y., February 14, 1969. · Zbl 0233.65022
[6] J. de Buchet, ”How to take into account the low density of matrices to design a mathematical programming package – Relevant effects on optimization and inversion algorithms,” in:Large sparse sets of linear equations, Ed. J.K. Reid (Academic Press, London, 1970) pp. 211–217.
[7] G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, 1963).
[8] G.B. Dantzig, ”Compact basis triangularization for the simplex method,” in:Recent Advances in mathematical programming, eds. R.L. Graves and P. Wolfe (McGraw-Hill, New York, 1963) pp. 125–132.
[9] G.B. Dantzig, R.P. Harvey, R.D. McKnight and S.S. Smith, ”Sparse matrix techniques in two mathematical programming codes,” in:Sparse matrix proceedings, Ed. R. Willoughby (RA-1, IBM Research Centre, Yorktown Heights, N.Y., 1969) pp. 85–99.
[10] E. Hellerman and D. Rarick, ”Reinversion with the preassigned pivot procedure,” Paper presented at the 7th Mathematical Programming Symposium, The Hague, September 1970. · Zbl 0246.65022
[11] H.M. Markowitz, ”The elimination form of inverse and its application to linear programming,” Management Science 3 (1957) 255–269. · Zbl 0995.90592
[12] W. Orchard-Hays,Advanced linear programming computing techniques (McGraw-Hill, New York, 1968). · Zbl 0995.90595
[13] D.M. Smith, ”Data logistics for matrix inversion,” in:Sparse matrix proceedings, ed. R. Willoughby (RA-1, IBM Research Centre, Yorktown Heights, N.Y., 1969) pp. 127–138.
[14] R.P. Tewarson, ”On the product form of inverses of sparse matrices,”SIAM Reviews 8 (1966) 336–342. · Zbl 0222.65050
[15] J.A. Tomlin, ”Maintaining a sparse inverse in the simplex method,” Operations Research Department, Stanford University, Technical Report 70-15, November 1970. · Zbl 0258.90027
[16] J.H. Wilkinson,Rounding errors in algebraic processes (Prentice-Hall, Englewood Cliffs, N.J., 1963). · Zbl 1041.65502
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