Forrest, J. J. H.; Tomlin, J. A. Updated triangular factors of the basis of maintain sparsity in the product form simplex method. (English) Zbl 0288.90048 Math. Program. 2, 263-278 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 54 Documents MSC: 90C05 Linear programming 65K05 Numerical mathematical programming methods PDF BibTeX XML Cite \textit{J. J. H. Forrest} and \textit{J. A. Tomlin}, Math. Program. 2, 263--278 (1972; Zbl 0288.90048) Full Text: DOI OpenURL References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.