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

90C05 Linear programming
65K05 Numerical mathematical programming methods
Full Text: DOI
[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.
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[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
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[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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